First of all, I am not a lawyer and can only speak from my own experience. My one question is: Have they signed a new lease in any form? If so, you will need to go through the eviction process.
Otherwise, in Ohio at least. I would hire a junk removal place to take all their stuff to a storage unit. It has to be stored there for 12 months I believe and you must provide them with the location. You can attempt to charge them for the storage unit rental, but wont have much luck I would assume. This is certainly an additional cost to you but part and parcel to the rental game. Before you transition to a new tenant, make sure you complete a move out checklist (you can download one as part of @Brandon Turner landlording book extras) and send it to the former tenant.
Not receiving 30 day notice from a tenant is a common problem. This is how we work around it. Collect a double security deposit. The first part acts a your security against damage, per normal. The second half goes to pay their last months rent, since you have their money on file, they call you to tell you they are moving in a month, and you use that money to pay their final rent payment. In ohio you do have to pay interest on any amount above a one month security deposit, but rates being what they are the cost is minimal and far outweighed by the benefit of actual notice.
@David Hildebrandt I enjoyed reading this advice, thank you! I'm a new investor in Cincinnati. I closed on my first multi-family (a quad) on July 16th and advice like this is invaluable to us new investors of the world.
If a lease is not signed and she vacated then that is the process for moving her out. Regardless of a verbal agreement that was on again off again.