You are taxed by Oregon only for the days you are actually working in Oregon. The instructions for line 7S say this
"Nonresidents—enter the amount you earned while working in Oregon for each job. If that amount differs from the Oregon wages on your Form W-2, request a signed statement from your employer verifying the number of days worked in Oregon and the total number of days worked everywhere. Keep this document and a statement explaining your calculations with your records. If your Oregon wages aren’t stated separately on your Form W-2, compute your Oregon-source income using the following formula:" See Instructions for Part Year/Nonresidents on page 14.
See the entire Line 7S instructions to get the formula and other notes.
In TurboTax, you will go through the Oregon interview answering questions until you see a screen with the title of "Oregon Source Income and Adjustments". Enter your actual Oregon amounts here (using the formula in line 7S above.
This will display on the Oregon return, and if you are ever audited (since what you enter will not match your W-2), be sure to do what the instructions say and get a statement from your employer.
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