Since you are still a California resident, you need to file a California resident tax return and an Oregon non-resident tax return.  Both California and Oregon will consider your income taxable, but California will give you a credit for the state tax you pay to pay to Oregon.  Between the two states, you will end up paying a combined state tax rate equal to whichever state has the highest rate.

When you prepare your state tax returns, start with the Oregon non-resident tax return first.  The program likes it better that way.