truth be told, i'm still a relative novice with only 22 years at the bar, so i'll defer to Jeff's experience and legal acumen. But just the same, know that the courts that decide such things might not agree with him. Take for example this summary of the law from Roth v. Dillavou, No. 2-04-0840 (IL 9/21/2005) (IL, 2005)
"A tenant who remains in possession after his or her lease has expired becomes a tenant at sufferance. (a case is cited here) At the landlord's sole option, a tenant at sufferance may be evicted as a trespasser or treated as a holdover tenant....A holdover tenancy is created when a landlord elects to treat a tenant, after the expiration of his or her lease, as a tenant for another term upon the same provisions contained in the original lease."
"Even when a holdover tenancy is not created, the parties' conduct may create a month-to-month tenancy (a case is cited)....Both a holdover tenancy and a month-to-month tenancy are governed by the terms of the original lease. (citation) However, a holdover tenancy lasts as long as the original lease term, while a month-to-month tenancy can last indefinitely, although it can be terminated on 30 days' notice.
N, you might be a holdover, maybe a month to month tenant. It depends.
You are right. Without a written lease extension or lease, you are on a month to month. It requires either party to give 30 days written notice. If you want to stay, you should approach the current owner for a lease. The new owner would be liable to the terms and conditions of said lease.
your original lease was for a set period of time (lets say, one year, but it was whatever you and the landlord agreed to). when it ended, you and the landlord either (a) rolled it over for another like term (i.e.another year) or (b) changed it into a month-to-month lease. if it rolled over for another term, you kinda have to ask that same question with each term expiration.
if you are on a term still, you have tenant rights until the end of the term. if you are on a month to month, then either side can (essentially) give the other a 30 day notice to end the tenancy.
don't be surprised if there is a disagreement between you and the landlord (new or old) about whether you are on a month to month, or term lease. ultimately, if it came down to an eviction proceeding in court, a judge would decide on whatever facts either side can present.
hope that helps,