The only confirmed home-grown omnimech the Ravens get is the Deimos, and the RATs seem to bear out that it is the most common assault class omni. Most of the rest seem to be leftovers that survived their exodus from the homeworlds or new purchases from the Sea Foxes and castoffs from the Ghost Bears.
I'll run through the list of omnimechs in the Front Line clusters mentioned in the RATs and where I think they probably come from.
Lights
Kit Fox - There is indication that the Uller was in production by the Ravens before their exodus and was likely their most common light omni.
Fire Moth - The good terms between the Ghost Bears and the Ravens probably led to a fair few of these in the Raven touman during the exodus, it's also not far fetched that the Ghost Bears would have sold worn out or otherwise cast off Fire Moths to the Ravens throughout the Republic era.
Mediums
Nova - A seemingly easy to maintain omni, with it's standard structure and armor, and indication that for a long period of time it was out of production and yet still was fairly common place. Those currently in the Raven touman were likely those to have survived the exodus of the homeworlds.
Stormcrow - Indicated to have possibly have been in production by the Ravens prior to the exodus from the homeworlds - supported by them being the clan that created the finalized design. This makes it likely to have been very common among Raven medium omnis, and it's efficacy in battle likely leading to the production of replacement parts in order to keep as many of them battle ready as possible.
Heavies
Crossbow - Likely salvage from their primary enemy in the homeworlds: the Steel Vipers. The lack of advanced materials being used in the design probably makes it fairly easy to keep repaired and battle ready.
Vulture - Among the most ubiquitous heavy 'mechs used by the clans, the surviving 'mechs are likely a combination of those coming with the exodus, as well as those sold by the Sea Foxes and Ghost Bears as they and other clans update their toumans with Mk IIIs and Mk IVs.
Karhu - Very likely traded or bought from the Ghost Bears or Sea Foxes.
Mad Cat Mk IV - Bought from the Sea Foxes
Vulture Mk IV - Bought from the Sea Foxes
Linebacker - Probably most of these are survivors from the exodus from the homeworlds, though purchases from the Wolves/Sea Foxes are entirely possible.
Cauldron-Born - Was among the Raven's more common heavy 'mechs according to FM3085 RATs. Possibly enough survived the exodus to remain common enough to make it onto the FM3145 RAT (if only barely).
Assaults
Deimos - The only confirmed homegrown omni, and it's frequency ratio on the most current RAT supports it's ubiquity among Raven assault forces.
Gladiator - Likely bought or traded from the Sea Foxes or Ghost Bears.
Kingfisher - Likely a combination of survivors of the exodus and more recent purchases from the Sea Foxes and Ghost Bears.
Now it's important to point out that RATs are not really indicative of the true disposition of the whatever force is attempting to be made through them. An example of this is the Raven Keshik, which is supposed to be 100% omni, though going strictly by the RATs, every weight class has the possibility of being a non-omni.
One other thing to point out is that the Raven touman has shifted even further into second line units than just their battlemechs, there are front line galaxies and clusters being noted to be using protomechs - though we don't know for sure if these are replacing 'mechs or battle armor. Assuming the standard cluster having a trio of 'mech trinaries the Raven Touman still only has about 325 omnimechs (this ends up being 48% of the Front Line Clusters and the entire 45 'mechs of the Keshik, though the ASF contingent could throw the numbers off in either direction depending on their make up).
Lastly, at least regarding the known touman, the Alliance has not shifted all their battlemech production to clan specs, the Cadaver being the prime example, where the version produced by the Alliance is less advanced than that produced by the Taurians - though the fact that the Alliance and Taurians are making the same design indicates there may be something going on there.
A lot of the above really shows a lack of ability to keep their production at the levels equal to a lot of the other clans, with very few of their omnimech forces likely being newer production and possibly being castoffs from better off clans. I perceive a large portion of the responsibility being laid at the feet of the clan choosing to slow down or even shut down (depending on how one reads it) the jumpship yards they rebuilt over Quatre Belle, had they kept them going at full steam they probably would have been better off financially and possibly even industrially (by selling Inner Sphere tech invaders, star lords and monoliths to whoever wants them, as well as increasing interplanetary trade among the Alliance worlds). Their choice to mothball a portion of the yards as well as not integrate themselves more fully with the Outworlders has led to their current state, at least in my opinion.
