You started off the year with NJ as your permanent home (your "domicile"). Your earnings are always taxable by your domicile state. Your domicile doesn't change when you relocate temporarily for school or work. So you remained a NJ resident for tax purposes when you were living temporarily in DC and VA. The question in your case is whether you became a resident of MD when you moved there. The answer to that depends on the nature of your move.
Scenario #1: IF your move to MD was a permanent move, then you became an MD resident when you began living there. In that case, you must file a part-year resident return in both NJ and MD, and allocate your earnings between the two states based on the number of days you were a resident of each.
Scenario #2: IF your move to MD is temporary and you intend to return to NJ, you'd only be filing in NJ. In this scenario, you don't become an MD resident, NJ remains your domiciliary state throughout the year, and ALL your 2016 earnings are taxable by NJ.
You don't have to file a DC or VA return in either scenario. DC has tax reciprocity with all other states. If you work in DC and are a legal resident of any other state, you do not have to pay DC income tax on your wages. Technically you never became a resident of DC because you lived there fewer than 183 days. Also, technically you never became a resident of VA, nor did you ever physically work in VA. Therefore you don't have to file a VA return.
For future, be aware that MD will consider you a resident for tax purposes if you live in MD 183 days or more during 2017.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
