I assume you’re talking 2nd Edition.
Axis powers with which the Soviet Union is at war may move units into or through any Soviet-control-led territories normally, regardless of where they’re located. Axis powers on the other map may not move units into or through any Soviet-controlled territories. Allied powers at war may move units into or through Soviet-controlled territories only on the map on which the Soviet Union is at war.
In your example, the Soviet Union is at war with Germany and Italy, but not Japan. German and Italian units may attack or fly over Soviet-controlled territories on either map. However, Japan must still treat the entire Soviet Union as a neutral power, and may not move units into or through any Soviet-controlled territories. Allied powers at war may move units into or through European Soviet-controlled territories, but not Pacific ones.
This is a slight change from the Alpha rules, and will be included in the upcoming FAQ.