My wife moved from Oregon to Colorado in April. I moved from Oregon to Colorado in December. My wife has 3 months of OR income, and 9 months of CO income. I have 11 months of OR income and 1 month of CO income. Can we file joint Federal and State returns?

Yes, you can file joint return.
For OR you are resident for 11 months and your wife is resident for 3 months. Report incomes earned while in OR.
Similar approach for CO.

Just to make it clear - you file as part-year residents in both OR and CO. You'll see on the forms that for each state you report your full year income, and allocate a portion of your income as being sourced in that state and hence taxable by that state.