My company rents an office in nyc, but our headquarters is in NJ. I will work and live in nyc. Do I owe nj taxes?

No - you only owe income taxes in the state(s) where you live and work. If you do not live nor work in NJ then you have no NJ income tax commitment. It does not matter where the company HQ is located. Your company should be withholding NY State income tax and NYC residential tax from your paycheck, and not NJ income tax.