The core story of the Fallout: Equestria "franchise" follows the adventures of the little mare Little Pip from Stable 2, under Ponyville. Little Pip's story begins when the secret romance of her young life and singer of Stable 2 - Velvet Remedy - approaches her about fixing her Pip-Buck (the obvious comparison to Fallout's PipBoys). LittlePip agrees, if stricken that her idol would approach her. However, things go south quickly when its revealed shortly there-after that Velvet Remedy somehow escaped. Much of the Vault immediately blames Pip for Velvet's disappearance, based on her ownership of her PipBuck that would have otherwise allowed them to keep tabs on their starlit.
Wishing to clear her name, LittlePip opts to escape the Stable in search of Velvet. This suggestion is met with hostility from the Overmare who says that if she leaves she could not let her back. Undaunted, she escapes her underground home - and the home for many others over the course of roughly 200 years - and sets hoof into the wasteland of the former nation of Equestria. What follows is an adventure in discovering friendship, secret plots, and the deterrence of evil, genocide, and simply trying to restore what amount of order Pip, Velvet, and their new friends can accomplish.
The Equestrian Wasteland isn't obviously just populated by the ponies descended from those unfortunate souls to have survived the spell-fire, or crawled out of the stables, but a plethora of other races.
High in the sky, beyond the cloud-curtain that covers Equestria lives the Pegasi civilization. Long having declared themselves separate of the ground the Pegasi have lived in strict isolation from the ground fearing exposure to radiation or disease (depending on your stance over Project Horizons, this could be greatly added to). And where civilization on the ground has stopped, Pegasi civilization has kept forward movement, even if largely starved of many resources that would be otherwise available on the ground for their use. Food shortages has put demands on the Pegasi to enforce strict population control to the point of homosexuality being encouraged among the population to keep excessive breeding in check. As well, the Pegasi Enclave work as a loose federated enclave between their giant mobile cloud-cities; sometimes built on the back of war-time sky-ward battleships.
Those of the Pegasi who would abandon the life-style in the sky or act in contradiction against the Enclave's politics are branded as Dashites and exiled to the wasteland below, with orders to shoot to kill if discovered otherwise. Dashites stem from the actions of Rainbow Dash - former Minister of Awesome - who according to the Pegasi committed grave treason against her race for advocating against sealing the clouds between the surface and them. This action forcing her to exile, and later possibly slain by her old friend Gilda acting as a mercenary.
There are then the Zebra. Long considered the proponents of the war that ended Equestria, the Zebra that survive in Equestria today are little-more than nomads. Zebra in capabilities are no different than the Earth Ponies. But the Zebra have in their culture and abilities a host of temporary magical augments passed down between the tribes. The exact stance on the use of talismans and native skill vary between the tribes, with the most ostracized being the practitioners of Dark Magic associated with the Stars and sky above; most often linked with Nightmare Moon in pony concepts (though, this later sentence here is something from Project Horizons, and may depend on your stance on that).
The Zebra during the war fought Equestria over supplies of coal and the gem trade. Lead by the Caesar in the city of Roam, the zebra and Equestrians butted heads over rights to gemstones to power their magic, and Equestria like-wise demanded their coal to fuel their growing industry. However, pride and a series of unfortunate events between the two ultimately mounted to full-scale war. Both sides never really having fought a serious war - the Ponies themselves haven't had major political conflict for over a thousand years - but they learned quickly over the years making blistering progress and leading to the rapid-pace developments of the technologies active in the FoE world. The Zebra are also the first to develop offensive mega-spell weapons - or balefire - after having healing mega-spells leaked to them from within the Equestrian government by Fluttershy of the Ministry of Peace; believing naivly that this would end the war. It instead only accelerated it.
The oldest continually surviving race of the wasteland are that of the ghouls. But it wouldn't be Fallout without our favorite zombies. As with the video games the fan-fic is based off of, the ghouls come in two flavors: those that have lost all reason and become animals and those that are still reasonable individuals. With many living well into two-hundred years old, the life-span of ghouls are long. And despite the natural necrosis the ambient radiation of the Wasteland only helps to heal many injuries not directly associated with cellular death from megaspell magic.
As with radiation in the Fallout world, the megaspells launched by Zebra and Ponykind also work unpredictably. Though they most-often kill on contact, the blistering magical heat of Balefire may also negate death completely, trapping a pony within their own body and rendering them a near-immortal ghoul. Though normal ghouls can be simply killed by suffering too much traumatic damage there are types much harder to kill. Namely those ghouls that have come to populate the former capital of Canterlot. These populations, known as Canterlot Ghouls, have been infected by the necromantic spell known as Pink Cloud which had been pumped thick into Canterlot until the city's inevitable destruction by the Enclave.
Pink Cloud is a megaspell of zebra design. Nearly always fatal, it has however worked the opposite and rendered some unfortunate citizens of Canterlot immortal. Canterlot Ghouls work the same as Ghosts from New Vega's Dead Money and the Red Cloud can be seen as the Pink Cloud's direct inspiration. Even down to doubly rotting and preserving matter it comes into contact with. However Pink Cloud - at initial contact - almost certainly renders flesh and clouds as one and melts the flesh into the matter around it, trapping ponies to choke half-deep in the cement or sealing doors completely shut. For the ferals, exposure to the Cloud has also enhanced their magical capabilities allowing them to take direct control of the cloud around them and using it like a weapon, if they are unicorns.
The population of Canterlot Ghouls is however effectively nonexistent after the course of events of Fallout Equestria. Canterlot was totally glassed by the Grand Pegasus Enclave slaughtering both the ferals and sane ghouls that lived within the city, ending the threat of being smothered by the city on entry, having one's head explode by radios, or being devoured by creatures that can resist the impact of bullets.
As a whole, the question of survivals of ghouls in the new wasteland his in question. The ghoul community as a whole in under-threat of extinction. With the firing of Gardens of Equestria by LittlePip and her companions the Wasteland was scrubbed clean of the ambient radiation and taint. As a whole the whole of Equestria was brought back to a neutral state. Such a thing was good for the rest of the world, but to the ghouls it was devestating. Without ambient radiation their healing functions cease and they find themselves incapable of rebounding after trauma or even slight damages. This as a whole means they effectively age again and can simply cease to live.
As a solution, Ditzy Do/Derpy Hooves - one of the pre-war ghouls to live and retain sanity (if without a tongue) - has organized the production and distribution of freshly irradiated water which is sold to ghoul communities across Equestria to fill their radiation need, though the practice is only one option and the only large-scale one. One that could be easily disrupted.
The last race worth covering for story's sake are that of Alicorns. Relatively new - in a way - to the Wasteland environment, the Alicorns are an effect of the experimentation of one of the few surviving figures from pre-war Equestria. Exposed to a chemical known as "Taint" - which apart from Mareposa and some other isolated locations is eerily constant in Equestria's background radiation - Alicorns are bred from unicorns. Those that survive the mutation with no unwanted mutation (such creatures becoming the Fallout Centaur with pony features) become Alicorns, slave to the will of the greater amalgation of collective personalities known as The Goddess.
The Goddess herself is mostly all of one pony who exerts absolute control of the mass of personalities: [The Great and Powerful] Trixie. Through telepathy and a collective consciousness she controls her Alicorns with a single-purpose: to convert all life of the Wasteland to her one singular, brilliant, race. She is however blinded by her own ambition, despite the coaxing of Twilight Sparkle - which is another quarter of her being - and doesn't notice that one of her allies - Red Eye - is proactively seeking a way to breed stallion Alicorns and that her own simply can not breed, which disturbs the other personalities of her being even if they keep silent about it.
Trixie and Mareposa are ultimately destroyed by a megaspell slipped into it by LittlePip, having erased her memory with magic prior to launching her grand plan and distributing only the relevant bits of the plan to her friends so Trixie could not predict her motives. This move liberates the bulk of her Alicorns leaving them to their own will as the scattered personalities seek a new refuge, mixing or finding no body to call their own. Many of the survivors find themselves citizens of the New Canterlot Republic, a product of Little Pip and friend's adventures once relative peace was restored. The NCR as well managed to research into gender-bending potions to allow the Alicorns to have families has they desired, though their offspring's magic is considerably muted in comparison to their parents (who themselves only specialized in one of three types of magic: shields [Dark-green], teleportation [Twilight-purple], Invisibility [Trixie-blue]).
The firing of Gardens of Equestria has also effected the Alicorn community. Prior to the fall of The Goddess alicorns could utilize radiation to restore their magical abilities or even provide a temporary boost and overcharge to their individual powers. But with a lack of concentrated radioactive pools and craters the alicorns are incapable of rapidly recharging or boosting their abilities, and so either remain stunted or most rest for longer between excessive bouts of magic.
Within the lore there are more races. Griffons, an instance of two-dragons - one more than familiar - Hellhounds - Diamond Dogs twisted by radiation and "Taint" and their augmented counterparts in The Hoof: Sanddogs, Robots, and so on. There's a wide diversity to fit whatever narrative you wish.
Beyond race, the story explores in some fashion war-time politics involving the failed assassination plot on Princess Celestia, which instead killed Big Macintosh and resulted in her abdication as Princess and the rise of six ministries ran by the Mane 6: Ministry of Arcane Science (Twilight Sparkle), Ministry of Image (Rarity), Ministry of Peace (Fluttershy), Ministry of Morale (Pinkie Pie), Ministry of Wartime Technology (Applejack), and the Ministry of Awesome (Rainbow Dash). Universally these ministries lead to the deterioration of friendships between the Mane 6 as they get drowned in bureaucratic duties and war-time stress, including addiction to dangerous chems and excess paranoia (Pinkie Pie) and the pursuit of family affairs and a maternal relationship (Applejack). The conspiracies of the ministries float in and out, revealing the greater scheme in the war effort (I could also mention Project Horizons here again and see how many cringe). The Ministry of Wartime Technology also later breads the Steel Rangers who as part of the old Equestrian Military (ran by that Ministry more-or-less) covets technology in the same way the Brotherhood of Steel did; this ideology later leads to a civil war and the formation of Applejack's Rangers which hopes to use technology in the virtuous way Applejack would have wanted (Though its leader and former prospective father to AJ's child dies).
There is then Red Eye, the enigmatic slaver from a Stable himself. Red Eye saw the necessity of sacrifice to achieve the industrial and societal means he thought necessary to the reconstruction of Equestria. He was a any-means necessary villain bested only by the Grand Pegasus Enclave. Utilizing mass slavery he sought to reconstruct the wasteland. He also dabbled heavily in alicorn experimentation and sought to make himself an alicorn.
He was a character who professed himself a savior, a paragon to the Wasteland. But he was in his methods cruel. It may be argued that he saw many of his actions sacrificial for his mission that he expected the same out of everyone serving him. It was this mentality that made him brutal in his methodology.
Ultimately, the story climaxes on an assault on the Pegasi military base at Neighvarro. The intermediary details are long and complicated, and include at least one case of a massacre by Little Pip so the above details are all that's going to be dumped. But revealed in part through dabbling in the memories of the old world its revealed the many cloud-height towers across Equestria are linked to a single installation that's been in two-hundred years of lockdown. This installation - the Single Pony Project - was a effort by the Ministry of Awesome to lessen the burden of resources on the Pegasi by establishing a network of weather control in such a way that a single pony may control the entire nation's weather, so long as the towers stand. The installation was locked, awaiting for Rainbow Dash or a descendant to unlock it; which Little Pip was not but found a way (involving Spike the two-hundred year old dragon).
LittlePip gains control, meeting the remains of Princess Celestia and her consciousness that she uploaded into the installation's computer. However, she did not have the power to actively use it and could only sit by for two-hundred years and watch in horror and agony the world below. The installation backfired for her, and ceased working. Realizing this, LittlePip knew she had to take control and did, plugging herself into one of the pods and assuming the roll of the SPP operator and ruler of the weather. She never went full Celestia, but maintained herself in the station.
Years later, she still lives there. Down below her new romantic interest, the DJ named Homage uses the SPP tower's role as radio towers to deliver radio broadcasts across the Wasteland and the first-person account of Little Pip's adventure on capturing Neighvarro. And at her journey's end she brought the light of the sun to Equestria proper, earning the title Light Bringer by the fledgling nations below, still trying to scrape together on the post-war ruin.
