File a part-year resident return for each state. Enter your W-2 as is. Allocate your income prior to becoming an HI resident to OR. Allocate the remainder to HI.
Since OR does not tax income earned remotely by a non-resident, you have no double-taxed income, and you will obtain a refund from OR on any excess OR taxes withheld.
The income you earned after becoming an HI resident is fully taxed by HI, and you (probably) were under-withheld for HI. If so, you will have some HI taxes due.
Since there is no double-taxed income, the "other state credit" issue does not come into play at all.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
