State tax filing

Yes, you can do the W-4 for California only.  You will be able to claim a credit on your Massachusetts return for any taxes paid in California while you were still a resident of Massachusetts.

This would ensure you are not taxed on any income twice in in Massachusetts as it will already be taxed in California.  

As far as your filing status, you can absolutely file jointly for federal and Massachusetts.  How you file your California return depends upon if you make the move to California or not during 2021.  If you do not move, you will be able to file in California separately as a nonresident and only report your income.

If you do move to California, you will need to use the same filing status as used on your federal return.  You would need to report the income from your wages and her wages, but will be able to claim a credit in California for any income also taxed by Massachusetts.  Once you become a resident of California, your income, regardless of state source, will be taxed on the state income tax return as you would not be considered a resident of the state.