Actions for unlawful or forcible entry are required to be brought within two years of the alleged action. O.R.C. 1923.01(B). It is ok if your landlord hand wrote the eviction notice as long as it contained specific language required by the Ohio Revised Code. Furthermore, in residential rentals, landlords are prohibited from "self-help" evictions. O.R.C 5321.15.
There are other common law claims that may exist in your case such as: conversion, trespass to chattels, tresspass, and possibly others. Each one carries its own statute of limitations. You should hire an attorney as soon as possible in order to protect any claims you may have from being barred by the statute of limitations.
If you have further questions please feel free to contact me.
Mr. Esposito is a Ohio-licensed attorney only. The information is not, nor is it intended to be, legal advice. You should consult an attorney for individual advice regarding your own situation. Answering this question does not in any way constitute legal representation. Contacting Andrew Esposito does not constitute legal representation, nor is any information you provide protected by attorney-client privilege until otherwise advised.