For income tax purposes you are a part-year resident of NJ and a part-year resident of AK. You will have to file in both states for 2017.
CORRECTION: You will have to file a part-year resident return in New Jersey. Alaska does not have an income tax, so you do not have to file a return there.
From what you wrote it's not clear whether you lived in AZ at all in 2017, or had any AZ income in 2017.
Your driver's license does not determine your residency. You became a NJ resident when you moved to NJ. You were supposed to get a NJ license within 60 days after moving there. You are supposed to get an Alaska license within 90 days of moving there, so you should probably be doing that by now.
