Yup, GDE is the answer.
Go to the technology tree and look at 'overview' (I think that's it). Towards the bottom-right you'll find 'GDE'. In 1940 this can be as low as 0.5, which means you need 1.6 divs to have the same def. as a div. with GDE of 0.8.
Consider also the massive advantage the Germans have in starting organisation. Given divs stop contributing to batle after 0 org. (or it might be 5, I can't remember), then this becomes significant. Assuming equal rates of org. loss, if you're starting with 50% and they have 90%, all your divs will reach 5% while the Germans still have 45% - at which point you will be forced to retreat.
On top of that there is the German superiority in leadership (generally speaking, if you'll pardon the pun....) and their HQ bonuses through their doctrine.
Combining these factors - GDE, org. and leadership - the Germans have a large advantage when attacking (plus the combat model favours attackers).
So what to do? Well, numbers for starters. USSR can produce divisions like flies, so do so! Secondly, Russian doctrine means you regain lost org more quickly (org regain is a function of supply and morale, and the USSR's doctrines lead to very high morale), plus you gain org while retreating, whereas the attacker loses it while advancing.
The thing is to cause the Germans to lose org and then keep them there. Having a staggered def line is a way to do this, as you can attack their units when they arrive in a new province with reduced org. Force them out, occupy it yourself, then retreat if attacked. Each time a prov changes hands it loses 50% of its infrastructure level, which then needs to be repaired over time (happens automatically). Low inf. = reduced supply level, which reduces combat efficiency AND reduces the rate at which units regain org. Use CAS on interdiction to attack org levels. Use TAC to hit infrastructure. Combining those will keep the Germans at low org values, thus reducing one of their main advantages. You, at the same time, will be gaining org much more quickly. Finally, fighting when they have low org will more likely increase casualties, and you have manpower to burn whereas the Germans don't. In other words, you shift the terms of combat to favour your strengths and nullify theirs.
Sorry for long post, but I suffered the same problem until I gave it greater thought through comparing the German/USSR strengths and weaknesses.
Cheers