No, you do not have to pay taxes in Oregon since you do not live or work in Oregon. Oregon does not tax work you do from outside of the state.
If you had taxes withheld from Oregon, you will need to file a return reporting income as $0 and the full amount of taxes withheld to get a refund of the amount withheld. For taxes other than income taxes, you will need to contact your employer. The transit tax also only applies to residents of Oregon, not nonresidents.
All income that you earn IS taxed by Idaho since you live in ID.
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