I would like to know what is the eviction process for a tenant in n.j. with no lease

New Jersey is 30 days notice and you have to give a notice explaining why
Something like this.
Notice to quit Free Form
If they do not leave after that go to your district court.
If they are behind in rent you have to accept it and let them stay if they come up with the money.

NJ has very strict tenancy laws. You can't evict a tenant unless it is for one of 16 very specific reasons. Check out LSNJLAW - Tenants' Rights in New Jersey Chapter Index