You were a guest until 10/15/15 and a month-to-month tenant from then on. With no written IOU for anything that occurred prior to 10/15/15 I don't see any judge awarding them $2000.
Assuming you paid rent on 10/15, 11/15, 12/15, and 1/15, it's clear that you were wrongfully evicted.
The Texas landlord tenant statute address termination of a month-to-month tenancy as follows:
Sec. 91.001. NOTICE FOR TERMINATING CERTAIN TENANCIES. (a) A monthly tenancy or a tenancy from month to month may be terminated by the tenant or the landlord giving notice of termination to the other.
(b) If a notice of termination is given under Subsection (a) and if the rent-paying period is at least one month, the tenancy terminates on whichever of the following days is the later:
(1) the day given in the notice for termination; or
(2) one month after the day on which the notice is given.
So, basically, they were legally obligated to give you one month notice.
Further:
Sec. 91.004. LANDLORD'S BREACH OF LEASE; LIEN. (a) If the landlord of a tenant who is not in default under a lease fails to comply in any respect with the lease agreement, the landlord is liable to the tenant for damages resulting from the failure.
2013 Texas Statutes :: PROPERTY CODE :: TITLE 8 - LANDLORD AND TENANT :: CHAPTER 91 - PROVISIONS GENERALLY APPLICABLE TO LANDLORDS AND TENANTS
Here are some options:
1 - Tell them one time to pound sand, then ignore them. Block their calls. Block their emails. Never talk to them again.
2 - Or, write them a letter saying you don't owe them anything because there never was a debt and if they sue you, you will counter sue for damages due to wrongful eviction and quote the statute in your letter.
One might say you also have the option of handing over $2000, but that's not really an option.