Tax is definitely due to OR. OR can tax all the income you earned after you became an OR resident.
You can take a credit on your OR return for taxes that were paid to a non-resident state on income that was taxed by both the other state and by OR.
It appears from what you say that NJ has taxed your full 2018 income (they withheld taxes all year). Therefore, your income AFTER the move was taxed by both states, and thus you can take a credit on your OR return for the taxes paid to NJ on that portion of your income.
So you'll need to determine 1) how much of your income was earned as an OR resident; and 2) how much tax you paid to NJ on that income.
NJ is one of the few states that tax non-resident remote workers, if the worker is working remotely for his own convenience, rather than the convenience of the employer. This topic is well-discussed here: <a rel="nofollow" target="_blank" href="
https://www.thetaxadviser.com/issues/2010/feb/apractitionersguidetothetaxationoftelecommuting.html">...
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
