If there was no agreement as to the the tenant's obligations while residing in the house. If the tenant damaged your property then you might have a basis for a claim. But if the issue is simply the cleanup, then you would be hard pressed to prevail on a claim where you want reimbursement for clean up charges.
This is not to be considered legal advice nor does an attorney-client relationship exist.
Yes. They would be considered a month-to-month tenant. You will need evidence of the damage and receipts. Depending on the damage and their ability to pay the judgment, it may not be worth the trouble.
Yes, you can sue them for any legitimate charges not covered by the security deposit.
The judge will expect to see proof, like pictures at the time of move-in and pictures at the time of move-out.
You will have to submit receipts from the vendors you used. Some judges don't allow the property owner to charge for their own time, only for the purchase of cleaning materials and replacement items.
You may be required to bring in the vendors to the hearing so they can testify as to their charges.
You should send a demand letter to the new address.
You can then sue the former tenants.
Did you send the statutory notice regarding security deposit within the 15- or 30-day timeframe? If not, then you may have to refund the security deposit to the former tenant.
Once you get a money damages judgment, they are often difficult or impossible to collect.
You may wish to join a local landlord group to discuss collection difficulties and how to protect yourself as a landlord.