Have had a family of 3 staying in our home for the past few months and we need them to leave but are refusing to leave. They have paid no rent, no utility bills in their name, and no signed agreement. We have asked them to vacate numerous times, giving them a month each time to vacate. They refuse to leave. What grounds do we have to make them leave.

It depends on the particular law of whichever state you are in. In general, you will have to give them a written notice and, if they fail to go by then, you would go to your local court and start eviction.

It does not matter that they do not pay "rent" or that there is no bills in their name.

You must give then written notice, and if they do not leave, evict them though the courts. Treat them like a renter. And you are the landlord

Each state has different laws, and some locales have more local laws too. So go down to your court house and get forms.