The idea that the Germans or Japanese wanted to "take over the world" is false, and a result of pop history and other nonsense.

Japan attacked the US in order to defeat the US Navy in a decisive engagement, and allow the Japanese a freer hand in Southeast Asia. They were never planning on occupying California, or anything like that. The "ideal" situation for the Japanese was to make a peace treaty with the US favoring Japan in which the US would not meddle in Japanese conquests. The Japanese were far more interested in securing resources (namely oil) in Southeast Asia than in occupying any American territory. They believed that a few rapid decisive victories against the US would knock them out of the war, and then they could go on conquering in the Pacific. They were wrong, obviously.

The Germans themselves did not have any plan to conquer the whole world, let alone all of Russia. They planned on occupying Russia's westernmost (and most productive) areas, while leaving land beyond the Urals as some kind of frontier. The lands they occupied would be settled by Germans and their allies, and the local population expelled, killed, or serving as an underclass - most likely a combination of all three. German occupation policy differed in every country they attacked, due to all sorts of reasons - some of these reasons quite pragmatic, others due to ridiculous racial policy.

For example, Poland as conquered by Germany basically ceased to exist. The land was annexed and a German General Government was set up in Krakow. Compare this with France, for example, in which Germany occupied parts of it to continue the war against the UK while Vichy France continued to function under a French government with a French military. Places like Denmark were treated rather 'nicely' due to a compliant populace and racial compatibility. The massacres you'd see in the East against the people the Nazis thought of as "subhuman" would not be seen frequently in somewhere like Norway. Nazi soldiers in Russia could get away with (and were encouraged to do) all sorts of pillage and murder while they would be harshly disciplined for trying this in the Netherlands, for example.

In short, it must be remembered that neither the Japanese or Germans had any plans to conquer the USA, let alone the rest of the entire world. The places they did conquer they oftentimes did not fully annex. They also had allies (Italy, Hungary, Romania, Bulgaria, etc) and were fond of setting up compliant puppet regimes. The idea of the entirety of Russia being occupied by German troops wouldn't have happened even if the Germans had won. You'd see plenty of other nationalities sharing the effort, from allies like the Italians and Hungarians to 'local' populations willing to collaborate like Estonians, Ukrainians, and many others.

If we're going to go full alternate history and assume an Axis victory, then the USA would likely have made a peace treaty with them that involves restricting the US from involvement in Axis spheres of influence without any Axis troops occupying any of the US. It would likely look more like the Cold War than "Man in The High Castle".

To clarify that:

I think that I remember, that Hitler wanted to avoid the USA joining the war at all costs and was therefore not amused about Pearl Harbor but he attacked russia, a country of a "similar“ size while the german troops were already spread around whole Europe and parts of e.g. africa.

How did anybody thought, that they could occupy these countries long-term?

The amount of troops needed to control the population would be insane or?