Welcome to landlording. 1st if your agreement stated a certain date of exit, then I would then proceed with evictions. Easy to do. Get forms online... month to month requires notice in NJ. Make in writing and document everything. Damages are your responsibility, but the security deposit should have been given to you from the previous owner.
Do not back off, you can always cancel the process. Being a landlord means you are in business and in business you have to make decisions. This should be the easiest although it seems as most difficult. Do not show emotion do not be mean, just be a the owner. You have the law behind you. The law takes time and most tenants know this.
Start the process it will cost approx $50 or less. and will be the best $50 you eer spend. You are in Gloucester county... http://www.judiciary.state.nj.us/gloucester/index.htm
Representing yourself in court http://www.judiciary.state.nj.us/prose/index.htm
Forms http://www.judiciary.state.nj.us/forms.htm go to the landlord forms.
Call the offices at the Gloucester County courts, they will direct you what forms need to be done and assist you with completing them. They will not give you legal advice. But Make sure you document eveything. Every conversation every letter... Keep a log so when you go to court the judge will know you are telling the truth . dont expect a complete decision the first time, but it will be favorable. This works, but sometimes takes time. Don;t get angry or show anger at the court just tell the facts. You can express yourself and the opposing parties unwillingness to cooperate.
As far as damages, I would hope the old owner gave you the security deposit. Log each damage done and take pictures. Hopefully you have pictures now so you show a before and after. I would also consider involving the old owner to provide proof of condition of property before.
All the landlord court will do is address the eviction and rents. They will not consider late fees or damages costs. Unless you have a lease that states these items are considered as "additional rents". Thats a whole different part of land lording when it comes to contracts. Damages will more than likely addressed in small claims. Landlord court will address it but the recovery will most likely be thru small claims. file that one right away too. As soon as you know the damages don;t wait till they are gone. You can always add to your claim when they are gone.
Landlording in NJ there are laws and tenants have certain rights. Adhere to these laws. Most tenants know their rights and if they dont they will learn them. So you need to be a step ahead. Here's some reading material
I have been in you position many times and much worse. Just hold your ground and "cover your butt" with documentation. Be prepared it will pay off.
Good luck. It's never a good thing when a tenant has to be evicted. I hated it every time. they have circumstances too, but always consider yours more important.
If you feel intimidated by the process see a lawyer. IT will cost you a little more but the process will be done correctly. Most tenants will leave when you have a lawyer. "Most" but the process is not difficult just time consuming. It's work!
Good luck and when you were buying I bet you never thought you would be a landlord!
If the tenant is on a month-to-month lease, that lease can be terminated by either party on 30 day's notice. If you were to terminate the lease--and, again, this isn't legal advice--and the tenant refused to move, you'd have to evict him.
If the tenant damages your property, the tenant would be responsible. Hopefully, when you bought, the security deposit was transferred from the seller to you. That should have occurred at closing. As with any tenant damage, your first recourse would be the security deposit. You might also attempt to collect in court, perhaps in small claims court.
The underwriter or lender have nothing to do with it. You own the house. It's yours. If it's damaged, it's your problem, and then you'd attempt to recover the money from the person responsible for the damage.
See a lawyer.
Hope that helps.