Yes, you must file tax returns in all three states (with a possible exception - see the info about reciprocal agreements, below.) Whether you must pay state tax to those states depends upon their rules.
You were a part-year resident of NY for a month and a half. Any income you earned while a resident of NY is taxable in NY, whether you earned it in NY or elsewhere.
You don't say where you lived for the rest of 2016. New Jersey and Pennsylvania have reciprocal agreements, which means that if you lived in one and worked in the other, you will only need to file a tax return in your state of residence. This assumes that you filed the proper form with your employer (NJ-165 if you were a resident of PA; REV-419 if you were a resident of NJ). If you worked in NJ but lived in PA, and only PA tax was withheld, then you filed the proper form.
