“In this case, how should we do the Fed tax return.”----> You can file your federal return either as MFJ or MFS; as you know, MFJ status provides more tax benefits than filing MFS, but you will need to weigh the pros and cons and decide for yourselves which is the best filing status.
“Also does I have to pay MA tax or my wife has to do NJ tax return.”---->MA is your home state and you are full year resident of MA, so you file your return to NJ as non-resident of NJ and claim state tax credit paid to NJ on your MA return. Your spouse DOESN’T have to pay any tax to NJ as she doesn’t have any NJ source income. You can file your NJ return as either MFJ or MFS. However, as said above, your spouse is not subject to NJ state income tax; she has no NJ source income. I guess you’d better fie your NJ return as MFJ for lower tax liability.
“Should we do join return for State or seperate tax return for each state”----> You can file your NJ return as either MFJ/MFS; you can also file your MA return as either MFJ/MFS. It is up to you; you can filer your federal return as MFJ/MFS, too, as said above.