The US doesn't care about your other nationalities. If you have citizenship or permanent residency in the US you need to file taxes (though despite what the other poster is saying, you may not actually need to pay any taxes).
If the nations have a tax treaty, you are usually not double taxed on income below some threshold. Last I checked, it was around the first $100k or so worldwide income, for US taxes anyway. After that, you are taxed at some rate, but I’m not sure if it is reduced at all or how different forms of income may affect this.
I believe the threshold, which is basically a big deduction, always applies if you meet the criterion (living outside the US). Tax treaties come into effect regarding whatever income you have beyond your deductions.
Good points. I should note that my foreign income was taxed and paid in the jurisdiction in which I earned it, so if you are not liable to pay foreign taxes on foreign income, you may not get the deduction advantages of a tax treaty to offset your US tax liability on worldwide income, as the intent is to not double tax. If you weren’t taxed on that income yet, the US may hold a tax liability on any and all income not already taxed, and it may be taxed a second time if said income exceeds limits.
That’s how I understand it, anyway. I hope to be corrected if I’m inaccurate as this is not my area of expertise.