Selling does not by itself cancel a lease. If you sell the occupied house to us, the lease typically stays with the house and we become the landlord, so tenants do not have to move out before closing.
If you would rather sell the house empty, Ohio Rev. Code §5321.17 says ending a month-to-month lease takes written notice at least 30 days before the next rent due date. A week-to-week tenancy takes 7 days' written notice. Read Ohio Rev. Code §5321.17.
Security deposits typically transfer to us at closing. Keep the lease and deposit information together so the handoff can be discussed as part of the written terms.