4 years ago, my mother persuaded my sick disabled sister to move in with her, so that they could help take care of each other. My mother has now relocated to another state and is trying to evict my sister from the home in order to sell it. My sister never paid rent to my mom ( home is paid for), but did help w/monthly expenses. In January of 2005, my mother stated to my sister ( and I overheard the conversation) wherein she said that she would NOT sell the house for 2 years, in order to give my sister time to recuperate from a very serious illness. In spite of that "verbal agreement" she has now placed the house for sale and is in the process of evicting my sister claiming "verbal lease violations". The only verbal agreement that I ever heard about was the 2 year not selling the house agreement. Can she do this?

Yes. In fact your sister is not really a tenant (she never signed a lease or paid rental). So she could be removed as a trespasser.

She can be removed, and even an agreement to not sale a house for a certain time, would not be valid, since any contract dealing with the sale of real esate has to be in writing to be valid.