Stat system - not likely - I will gauge whether any submitted CS are overpowered and I will tell anyone if their character can be bumped up a little. However, not everyone has the same capacity to learning nor do we all have athletic bodies or quick wit. Some people may simple be more powerful/'stat high' but that doesn't count for much when they make a bad decision
Yeah, I highly recommend staying out of the demonic and supernatural world entirely. You don't have to screw around with the rules to compensate for stuff. As for stats, you could pick a few of the S.P.E.C.I.A.L. perks (Strength, Perception, Endurance, Charisma, Intelligence, Agility and Luck) from Fallout, but people get to pick only one or two.
In fact, just make a list with descriptions.
Strength: Can lift larger objects, kick open wooden doors, and carry more belongings.
Endurance: Can keep going in adverse weather conditions, run longer, and last longer without medicine when injured.
Charisma: Can talk others out of giving up supplies or not attacking you.
Agility: Can climb faster, scale larger obstacles, and are more likely to evade gunfire.
Luck: Can find more ammunition or extra food when scavenging, have a better chance of finding resources they are searching for, and find resources more relevant to them (if you have a shotgun, you will find more shotgun ammo than other kinds).
That's five, so maybe pick two of them. We the players are responsible for being realistic and limiting ourselves. Like, I have luck, but I only find a handful of ammo, not a box of it. I have agility, but I could still get clipped by a bullet from an automatic weapon. I have charisma, but I won't convince a whole group of people. And the GM will have the final say anyway, obviously.
If you have other ideas for the list, post them (I couldn't think of any for Perception and Intelligence). Or scrap the whole thing, it's up to the GM
@Vermillion