I would give them 30 day notice, posted properly as per Fl law. Then if they don't move in that time frame, I would file in court to evict them. If they have no lease then they are at best month to month tenant. Who did they pay the last due rent to? When was it due? I would not just take them at their word they will be moving out on the date they gave you. I would enforce the date. You should try and get inside to get pictures of the condition now. As there is a good chance they will trash this place before they leave. With pictures you might have a chance to sue for damages. But you may never collect. You should have never bought this place without the seller empting the place first. Or at least with a lease with current T if you wanted it for income property.