The Virezhir military is composed of the Exarchate forces (a mix of Imperial Authority Tagmas and hosts raised and paid for by the Exarchate's government) and the noble levies (any house controlling at least a system has the right to maintain "auxiliary forces", which is essentially an excuse for them to maintain private armies, and fleets depending on how wealthy they are).

The Rankovs control a few of the older and more powerful ships through the Exarchate Fleet, but not that many and certainly not as part of their own private forces. Furthermore, in their drive to make themselves less dependent on outside support, they've endeavored to develop a native military industrial complex. And while they're still dependent on outside suppliers for some of the more high end materials and industry, they can field a fleet with a reliable core of flexible ships.

On the ground, both the official army and the Imperial Tagmas rely on a combined arms approach. Mechanized infantry cooperating with armor, artillery and air support. Boring, I know :p, but the reasoning it's that this kind of boring works well in most cases. There's a cadre of special forces and specialized divisions for things like desert or jungle warfare. Noble militias are also used in these cases, as many of them like to field elite specialized regiments for prestige reasons.

The militias themselves vary in organization and quality. Depending entirely on the resources available to the house that raised and maintains them. I'm taking inspiration in the Imperial Guard from 40k for this, with specialized regiments dependent entirely on the means of the planet that raised them.

Also, genetic engineering is big in Virezhir. In both civilian and military spheres. For the troops, this means that most noble houses are able to pay for at least some minor treatments for their retainers. Slightly stronger soldier, slightly faster reaction time, that kind of thing. The rich ones can field greatly enhanced troops and genetically modified combat beasts. The Exarchate Army fields the best of them as their elite of the elite. Used sparingly and carefully because though very effective, they're also very expensive. The combat beasts, however, are relatively easy and cheap to produce, making their use more wide spread.