There are so many legal issues involved here that I would strongly advice you to speak with a landlord tenant attorney. Basically what is clear is that you received some sort of benefit so it is likely you'll have to pay something. The question is how much. You are at least in a month-month tenancy, so follow the notice rule for that "exit". I assume if the amount involved is substantial enough, the landlord will file suit either based on breach of contract or in equity.