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There are two basis principles for taxing the income - based on the income source and based on the residency of the recipient of the income.
If you are working in WA - that income is considered from WA sources and generally would be taxable on WA state tax return - however - Washington is one of a few states that does not tax individual wage income - so lucky you - that income is not taxable.
If you will become a resident of OR - your income would be taxable as for a resident - regardless of the income source - and your WA wages - will be taxable for Oregon.
Oregon has three income tax rates: for instance for single taxpayer - you will pay 5% on the first $2,900 of taxable income; 7% on income between $2,900 and $7,300.and 9% on income above $7,300.
Let me know if you need any help.