You worked and earned income in OR. You file a non-resident tax return for OR. You have no conflict/tax issues with WA, since WA has no state income tax. When you prepare your federal return you will indicate that you earned income in another state (OR) and it should give you a screen to indicate which months you worked in OR. That information will flow to the state return you need to prepare for OR.
https://ttlc.intuit.com/questions/2895920-why-would-i-have-to-file-a-nonresident-state-return
You can still use Deluxe; preparing a non-resident state return will not require you to upgrade to a higher version of the software.
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