If the lease has expired and the tenant has been given proper notice to quit, the tenant becomes guilty of unlawful detainer and may have to pay the landlord double the rent for as long as the tenant holds over.
So I'm going to respectfully agree with Steve as he may be speaking on laws in NM and not NJ. Again, consult an attorney. You can usually find a free one at the Legal Aid Service in your county. Good luck.
1. The general rule is that month to month leases can be terminated without cause by giving proper notice.
2. The exceptions to the general rule include termination for an improper reason or a reason that violates law or public policy.
3. Do you have pre-paid legal insurance? If so, give them a call. You might also try the landlord-tenant hotline in your area.