A complex game and probably best to get help on Steam forums for strategy.
If you are still learning the game mechanics, I suggest just playing Germans since they are slightly powerful versus the Russians. The Russians require a lot of experimenting with because there is a lot of nuance in the usefulness of their troops and their value versus Germans.
Just tried the Germans with my usual settings vs. the AI (Mechanised Infantry commander, the one with Assault Grenadiers) and lost pretty much as quickly, and for exactly the same reasons (lack of ability to contest territory, inability to focus on map control and combat simultaneously, inability to deal with armour) as with the Soviets. I'm coming to suspect that much-touted balance problems in favour of the Germans are largely or wholly illusory.
Granted my teching was slow due to unfamiliarity with German tech progression, but basic unit combat is the same, as is map control (although I believe a common tactic is to build bunkers, which I neglected), and in recent games I've found I need to focus less on micromanaging Soviets (capture point, build sandbags, sit there) than SMG-touting Germans and Grenadiers/HMGs that need to react with lightning speed to avoid Molotovs.
Possibly for players with a certain basic level of micro the Germans perform better.
1. only play 3v3 or 4vs4 against real people, and check with your team-mates for what DLC to get and what units they are rushing. A lot of Soviet commanders are situational and best as unique picks to support the other commanders.
I have all the commanders having got most in a sale and grabbing the most recent two when they were free, and no interest at all in team games - I don't know why these seem to dominate most casts (and discussions on the CoH 2 forum) when the game is supposedly designed around 1v1 and this is the typical play mode of RTS games more generally.
Besides which, adding an extra variable that's difficult to manage (at least for someone mainly used to single-player gaming) - coordination with a team mate - is neither likely to be fun nor a great way to learn a system.
2. Soviets have to push aggressively early in the match, especially to control or deny gas points, while holding onto a majority of victory locations. It is totally okay to rush past neutral areas with a sizeable force, if only to destroy a fuel depot, or to neutralize and mine a fuel depot.
I never had any answer on other forums about use of caches - as far as I can gather they aren't commonly used. The map I'm practicing on is Crossing in the Woods, where holding the fuel points can be very difficult as they're at the corners of the map. I did start playing a lot better once I learned to be aggressive, but I still end up losing territory while I'm contesting somewhere else - something I only seem able to manage if I can destroy enough enemy units early so that the enemy doesn't have the forces to do that.
Unfortunately I'm able to do that more by luck than judgement: I've only won a single game against standard AI on that map, and have lost almost half a dozen since.
3. If you want to control the field early, rushing Penal battalions with flamers in scout cars (the so-called Clown car strategy) is pretty viable. However it is easily countered by German armored cars, so you have to focus on denying fuel depots from very early in the match (like minute 3, I guess).
Yes, I have taken to doing this but find it generally difficult to manage due to the micro involved (usually I'll use it once then it will sit rather uselessly on a point for a bit), and to get the unit out before the car blows - even with a conscript squad for protection this nearly always happens at some point, though I've had more success with them against humans than against AI (which is much less likely to garrison buildings and so get flamed, and obviously has good micro). I definitely felt the lack of this option when playing the Germans, though.
4. Doctrine troops (e.g. Guard, buffed conscripts, etc...) are nice, but always situational to what you and your allies are rushing, and what the Germans are rushing. If you need help in controlling fuel depots early versus infantry, I'd say you can't go wrong with Partisans (cheap, easy to get, MG42 troops). Don't over-specialize in any doctrinal troop, and keep some conscripts nearby in reserve to keep the doctrinal troops in the field without retreating.
I loved the idea of Partisans (and they're thematically nearly right), so they were one of the first doctrines I tried - once again, though, they proved very micro-intensive as I had to shepherd the fragile squads around behind the lines.
6. Use snipers with hold fire orders, and scout cars, as scouts to locate targets for armor and artillery.
Trying this has usually lost me both - once again, a key issue is my poor micro since other than Starcraft (which doesn't require good micro at my level) I'm not used to playing real-time games (well, there's Diablo, but that's just button-pressing).
7. For most matches, plan on rushing about 2 to 3 tank destroyers, unless you are feeling lucky or visibly controlling the petroleum on the map. If you seem to be denying armor builds to the Germans, then a wolf-pack of T-34 tanks is pretty nice. Otherwise a back-up T-34 or two for ramming an armored vehicle is helpful for the tank destroyers sometimes.
How do you obtain fuel for that? I never have fuel to build both T3 and T4, and if I ever have the fuel to get a two T-34 call-in (plus my usual SU-85s) in even a fairly long match, I've had uncontested control of both fuel points for so long that I don't need them and the game's won anyway.