I've played a couple of PBEM games as Axis, and yup, rolled up China and Russia. So I tried as Axis against AI. I was able to defeat the axis by 1944. How?
as suggested above, double chit inf. But don't forget Command and Control. level one at least.
Your HQ's build up experience, which makes the units under them better. while not as important as inf level, it becomes so later. When German inf at level 2 fights Russian at level 2, being led by a leader with 3 experience stars, they will wipe you out...
For the russians, don't bother with any upgrades to aircraft, etc, save that for once your inf front stalemates (in 1943 for me). once you have inf research, and command and control, arty is your next priority. The US and Brits holding and pushing into north africa and then italy is what turns it around for the russias, as german strength bleeds out.
So how to survive till 1943? Dig.
I pull back and make a line around Sevastopol and Leningrad. Make sure you have both engineer units making fortresses. And make sure you have Arty (I like rockets) and a general at the heart of it. replace and reinforce, holding on. If your fortress gets close to finishing, then start in front of Moscow (though I never needed to).
In the south, you CAN counter attack the allied Romanian, Italian and Hungarian units. they are typically pretty weak and a Russian Army at level 2, or in winter will do lots of damage.
They are also more expensive for the AI to replace, so if you can, knock them down.
In China, do similar, keep your units in fortresses, behind rivers, with a leader, and dig around chungking. If you can get some arty do so. later, when india is in, I found I had enough str to move into china, and take back burma/thailand.
So you leave Moscow and Stalingrad to their fates? Also, how do you deal with spawned units at start of Barbarossa?