"If you have any questions regarding landlord-tenant issues, leases, or other personal legal assistance matters, contact the nearest military legal office for assistance."
Military Housing Clause
I keep reading that you should have a military clause in your lease which does or should address this issue. *Does your lease include a military clause? Did you sign one? Do you have a copy?* It's usually not a big problem when you have orders: enter service, TDY, PCS. Checking around online, I found some information about moving to base housing in Hawaii, Florida and Virginia but not NJ.
I don't know where you're located but read numbers 5, 6, 7 and 8 on this form and contact your legal office.