Does my husband's stepfather have the right to kick us out?

Sounds to me as though you and your husband are tenants in his step father's house--that will be the step father's argument. That being the case, you are entitled to prior notice of termination of agreement IAW UT law. Of course, you and your husband believed you were paying on your own home--as a result of an oral agreement. However in most states, something called the Statute of Frauds (SOF) prevents oral agreements for real estate matters. The Statute of Frauds is basically the idea that the courts do not want to allow for the possibility of a fictitious agreement between two parties being proven by perjury so they made some issues subject to the Statute of Frauds. The sale of land is one of those special issues subject to the SOF. In your case, the SOF would likely apply and the agreement purported to exist between your husband and the father in law would probably not be enforceable. That leaves you as tenants on his property. Since it would appear you don't have a lease agreement in place, you are likely in what is considered an 'at will' lease. In most states, that means that either party can terminate the agreement for any reason, or no reason, at any time--so long as proper notice is given. In some states that notice is 30 days, some 28, other as little as 15 days (I am NOT a UT attorney and do not know what the notice requirement is in UT, but I recall it as LESS than 30 days written notice. Recommend you contact a UT landlord tenant attorney IMMEDIATELY to determine if there are any grounds you may have to defend yourself in a termination of agreement (eviction) notice from the step father (also, as an aside, I would find it hard to believe that the step father was not fully aware that he was the owner and his step-son and daughter in law had no property rights in the house).