And in almost every case they invaded countries with less wealth than they had, the have-nots taking from the don't-have-a-pots.
Not really. The USSR was actually having a bigger economy than Germany or Japan. (Much as its people were individually poorer, it could produce more armament than Germany.) And Japan actually wanted to invade the USSR too, until they got a first hand demonstration that they're not ready for that.
Japan also invaded territories owned by, for example, the UK and at least tried to have a go at territories owned by the USA. E.g., Midway. You may have heard of the battle there. Both were much bigger economies than Japan, and in a far better position to throw immense resources against them.
Also, both Germany and Italy actually thought they could invade the UK colonial lands. You may have heard of the Afrika Korps. That's what that was about.
Germany also actually thought it could take on the UK mainland at one point, which, again, was a bigger economy than theirs, even if dependent on overseas convoys.
Italy also technically took part in invading France (and promptly had their ass handed to them), and the USSR.
Plus, you see examples that are actually the not-even-have-a-pots think they can duke it with the big boys. Like, Romania actually took part in invading the USSR. I mean, Romania... really? I just have to wonder, if you'll pardon my Klingon, dafuQ' were they thinking.