If the total amounts in W-2 Box 16 for Oregon and California together total up to the figure in Box 1 (which they seem to do, to the last penny), then it would seem that's how your employer intended the W-2 to read. It's certainly not incorrect to report wages from a multi-state employee this way, so let's take the W-2 at face value then and assume that it is correct.
If so, you will want to begin your tax return, in the Personal information section at the beginning of the program, that you are an Oregon resident, but that you "made money in another state" which in your case is California. This will cause the program to generate a full-year Oregon resident tax return for you, as well as a California nonresident return. This is correct and how you should report your income at a state level. You can continue to enter your W-2, just as you have it, into the software.
As an example of these steps, I've created for you a series of screen-capture images to demonstrate what this should look like in the TurboTax software when done correctly. Those images appear directly beneath this text; simply click them to open.
All of your income (earned everywhere) will then be reported on your Federal and your Oregon state return. Only your California-source (or wage) income will be actually taxed on your California state tax return. You will continue to finish your federal return normally, and make sure that you pass the "error check" at the end.
But, you're faced with the distinct reality of being taxed by two states on the very same income (i.e. "double-taxed"). How does this get resolved for purposes of tax fairness? Well, you should be eligible for a state tax credit for taxes paid to both states on that same item(s) of income, which consists of your California wages and any other income you may have from California sources. TurboTax will handle the math, and walk you through the process mechanically. Please just be absolutely sure, however, to "sequence" your tax returns in the necessary way for the software to work properly with the state tax credits. In other words you'll want to do the following:
1) Finish your entire federal tax return, and make sure it passes the TurboTax error check
2) Complete your resident Oregon state tax return
3) Complete your nonresident California state tax return
Please note that steps 2 and 3 are exactly "backwards" from the normal way that this process works in TurboTax. Typically, you see, we advise that the nonresident state be completed before the resident state return. However, the Oregon Department of Revenue has a "special relationship" with just (4) other states: Arizona, California, Indiana, and Virginia.
For those (4) states on this short list, which you will notice includes California, the standard ordering for state tax credits on double-taxed income is exactly reversed. Instead of taking an Arizona taxes paid Credit on your Oregon (resident) return, you'll instead be taking an Oregon credit on your California (nonresident) state return.
Is that especially confusing, you ask? Yes, it most certainly is. But it is also the application of current interstate tax law.
Hopefully this answer will give you all the information that you need to correct file your tax returns, and thank you for asking this important question.
