@noviceattax for me, then you are going to file 'part year' residence in all three states. Again, I would just report to each state the amount of income that is stated on the W-2. Presumably your W-2 shows three states, right? Assuming you are going to do this tax return in TT, just answer the questions in the prompts and it will come out correctly. There is no 'double taxation'. You will only report the income earned in each state to that state.
for that last NJ paycheck, you were living and working in NJ when you earned that money. Yes, you could make the case that you were living in CA when it was received, but then you are not going to report on your tax return what is listed on the W-2. That risks questions and audits from NJ - to me - not worth creating that headache, even though it may be technically correct to list that last paycheck as earned in CA. (CA is never going to know and won't question why you are reporting more income than the W-2 states - they are glad to take your money!)
On the repayment, can you go through that again?
When you received the bonus, which state were you living in and which state W-2 is it listed under?
When you repaid the bonus, which state were you living in and which state W-2 reflects the repayment?
what is your concern? the fact that this is all within one tax year makes it not complex.
