Your best bet is to give them a 30 day notice to terminate their tenancy. You don't need a reason. Give them the notice before the first of the month and tell them their tenancy expires January 31st and they are to vacate the premises and leave it broom-clean. If they fail to move by that day, give them a 3 day notice. If they fail to move after the 3 days (really 5 days - don't count 1st and last day), you can file a forcible entry and detainer in your local eviction court. They will have forms and instructions.
Actively practicing law in Texas. Inactive licenses in Arizona and Georgia. All answers are general in nature and no attorney/client relationship exists in this forum.
The easiest thing is to probably end the month to month lease by giving the proper notice. If that is not an option, to the extent the trash violated any city laws/ordinances, the leases typically address violations of laws as a lease violation.