Historically, there was no chance-with OTL's Soviet Union's leadership-to have a real USSR Axis alliance. It's probably one of the great What Ifs of WWII in terms of seeing how such a scenario would play out.
Go full NazBol/Strasserist, align with Germany against the Anglo-Americans. WWII thus sees a War of the Wolves (Nazi Germany, USSR, Fascist Italy, etc) vs the Whales (United States, United Kingdom, Imperial Japan, etc).