OK, I have been in contact with a few russians to have the names verifiyed and this is what I came up with. Most of them are the same as before, but not all:
ARMY/GROUND:
Rifle Division - Strelkovaya Diviziya
Motor-Rifle Division - Motostrelkovaya Diviziya
Cavalry Divison - Kavaleriyskaya Diviziya
Mechanized Division - Mekhanizirovannaya Diviziya
Tank Division - Tankovaya Diviziya
Airborne Division - Vozdushno-Desantnaya Diviziya
Naval Infantry Division - Diviziya Morskoi Piekhoty
Mountain-Rifle Division - Gornostrelkovaya Diviziya
Militia Division - Diviziya Opolcheniya
AIRFORCE:
Fighter Squadron (Regiment) - IAP / Istrebitelniy Avia Polk
Bomber Squadron - BAP / Bombardirovochniy Avia Polk
Assault Squadron - ShAP / Shturmovoy Avia Polk
Long Range Bomber Squadron - Avia Polk Dalnih Bombardirovschikov
Transport Squadron - Polk Transportnoy Aviacii
Naval Bomber Squadron - Avia Polk Morskih Bombardirovshikov
Torpedo Bomber Squadron - Avia Polk Torpedonoscev
NAVY:
Destroyer Flotillia - Flotiliya Esmintsev
Submarine Flotilla - Flotiliya Podvodnyx Lodok
Transport Flotilla - Transportnyi Flot
And the numbering of the units should be like this:
"Divizya" is feminine and would be called "5ya Strelkovaya Diviziya" or "17ya Tankovaya Diviziya".
"Polk" (and "Flot" to I presume) is masculine and should be written "3y Istrebitelniy Avia Polk" or "11y Podvodniy Flot".
The word for "Guards" also change if the subject is masculine or feminine. If masc. it should be "Gvardeyskiy" like in "5y Gvardeyskiy Istrebitelniy Avia Polk" and if fem., "Gvardeyskaya" like "4ya Gvardeyskaya Motostrelkovaya Diviziya".
We also might want to consider abrevations for some of the names, but I'll leave that for now.
Oh, this should BTW be considerd a "Beta"

I'm just posting it to get some feed-back... And I'm getting more info in..
EDIT:
1. Changed Vozhdushno (Airborne) to Vozdushno.
2. Changed Eskadra Kreyserov (destroyer) to Flotiliya Esmintsev.
3. Changed Podvodniy Flot (submarine) to Flotiliya Podvodnyx Lodok