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I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
When there is no written lease, Ohio law requires a tenant to give notice of the intent to move at least 30 days prior to the end of the month. Ohio Rev. Code, Section 5321.17. You are not required to give 60 days notice even if the original lease required it, because that lease expired. If you're giving notice now, you would be obligated to pay rent for November. He can apply any security deposit you gave him to that amount.
Legally, it's not considered harassment to call someone you believe owes you money. But you are free to show the landlord the statute, explain why you're not giving him 60 days rent, and ask that he refrain from contacting you again. You do not have to answer the phone when he calls (and can even download set your phone not to ring or to play a special tone when he calls).
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