Legal Question in Real Estate Law in Illinois

There are more "facts" needed, but based on what you have here it would appear to be an oral, month-to-month tenancy that you can terminate on a month's notice.

The only issue would be what about your roomies, because the way it looks is that the 3 of you rented "together" and that could leave the remaining 2 liable for the entire rent, even if it is just for a month, and that sounds like something you'd have to make up to them.

Without a written lease the landlady would probably say she intended a lease of one year (therefore avoiding what is called the "statute of frauds" that otherwise requires leases for more than a year to be in writing) but she'd also have to explain the showings and failure to deliver a lease document. I would argue she knew all the time that all she wanted was either somebody to carry the load until it sold or to be a tenant for an investor buyer and she wanted to control the situation and never intended to give you 3 any kind of long term lease. The problem is what you may have thought it was going to be -- a year's lease -- but again the argument appears to be (without more like correspondence, notations on any rent check, lease application for a year term....) it became quickly obvious that was not the deal and you 3 were duped. No guaranties -- if you want a more precise opinion, bring any and all documents relative to the renting process (application, letters, emails, notes, etc., rent and security deposit checks....) to an attorney who can more clearly assess the situation.

Alternatively, before doing that you might try demanding the lease you wanted, because she might just back off, or you could control the situation better, but then enforcing it may also be an issue.