Short answer...

If you legitimately live in another state and can prove it (yes you have to prove it), then you don't pay taxes in CA/NY in that case. As long as you follow all the rules. Might have to pay some small fees for local worker benefits such as STD, but not income tax.

If you move overseas you could be subject to full state taxes in your last state of residence indefinitely. As you are considered to be "anchored" there while abroad. Unless you renounce US citizenship. So better to firmly establish residence in a non-tax state before moving abroad.

Be aware that deep blue/high tax states are very aggressive about pursuing their subjects who try to escape and take their money with them. You need to understand all the applicable rules and comply. They are very good, and aggressive, at catching you otherwise. If you own a house, or get a W2 for several hundred large in their state, you are on their radar.

Long answer.. talk to a good tax accountant with experience in these issues. It's complicated and can vary by state, although federal law will generally protect you if you move to a free state such as NV/FL.