It depends, but it is possible that New York taxes this income. If you were telecommuting to your New York office (working from home), New York does consider this to be taxable income to New York. If this is the case, then you file a New York Part Year/Nonresident return, and you will designate (or allocate) 25% of the income as earnings as a nonresident. You will prepare this return first.
Then, you will prepare an Oregon part-year resident return for the same income over the last 3 months. This is because Oregon will also tax this income, but they will give you a credit for the tax you pay to New York on the same income.
However, if you were not telecommuting from home, then New York may not tax the income. In this case, you file part-year returns to both, and you will have to allocate in New York the portion of income (if all of the box 1 income on your W-2 is showing up in Box 16 of the New York tax information line on the W-2) that was not earned in New York. You may use percentages for this, or actual amounts if you have them. Here is a screenshot of the screen you will use that initiates reporting this:
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