You have an option. Both California and Oregon give you the option to file separately or jointly. I personally would recommend that either you decide to file a joint return in both states or separate returns in both states.
What is the difference? If you decide to file joint returns for each, your total income is factored in to determine the state tax for each. In other words, both California and Oregon will determine what your tax would be on all of your income in that state, and then prorate the amount of tax based on the percentage of the income earned in each. So let's say the spouse in CA earned 40K and the spouse in Oregon earned 60K. Both CA and OR determine how much they tax a married couple on 100K of income, and then CA will prorate the tax to 40% of that amount and Oregon to 60% of the Oregon tax of 100K of income.
If you file separate returns for each, CA will only tax the CA income (at the married filing separate rate), and Oregon will do the same. Chances are the end result will be fairly similar, but the recommendation is to use the result that gets you the lowest tax liability (or largest refund).
To file a joint federal return and separate state returns, it is recommended to use desktop software. Please see this FAQ for more information: https://ttlc.intuit.com/replies/3301995
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