Your landlord has given you insufficient notice.
You are entitled to 30 days Written notice to vacate in Ohio (see: http://codes.ohio.gov/orc/5321.17). If the landlord does not give you proper notice, he cannot do anything to force you from the property (he can file an unlawful detainer (eviction) action, but it should not be granted.
You can try to avoid an eviction action in court by contacting the landlord and telling him that his verbal notice is insufficient and that you are not willing to vacate prematurely (demand proper 30 days written notice), which will give you some more time.
Furthermore, if you get to the end of 30 days and you cannot find a new place to live, he cannot simply force you out, he must go to court and get a judgment of possession against you. This takes time (especially if you appear in court and defend the action - do not simply let him get a judgment "by default" (what happens if you don't show up). This can give you an additional 30-60 days depending on the local courts and sheriff's office backlog.
The overall process looks like this:
"Eviction" is a word that is often misused and it leads to a lot of confusion, to help, here are the steps in terminating a tenancy:
Terminating a tenancy-
1) Notice: The first step in any termination is giving notice, the landlord can simply give notice that they no longer want the tenant to live there (this is usually 30 days, or 60 days, and it can be done for no reason whatsoever, there is no fault, and while the tenant must relocate, they are not being "evicted" and there is no blemish on their rental history), they can give a "notice to pay or quit" (usually 3 day or 5 day depending on the state, and the tenant has this amount of time to pay rent that they missed or move out), "notice to "cure or quit" (the tenant has breached the lease - broken something, noisy, etc. and must stop it or fix it within the notice period, again 3 days, 5 days, or 10 days), or a "notice to quit" (this is a 3 day or 5 day notice that says the tenant has messed up so badly they can do nothing but move out within the notice period - there is no chance to "cure" - this often happens when there is illegal activity on the property).
2) Unlawful detainer/forcible entry and detainer (this is the legal proceeding where the landlord goes to court and sues the tenant to get possession - the tenant has an opportunity to appear and defend the action, common defenses include improper notice, breach of the lease (such as failure to maintain the property - "inhabitable conditions"). If the tenant answers the complaint, the parties can take "discovery" from one another and get additional information before a court trial before a judge.
3) A judgment of possession/writ of eviction - if the landlord wins the trial, they get a judgment of possession and the court will issue a "writ of eviction."
4) Forcible eviction - this happens when the Sheriff or Constable serves the writ of eviction - some jurisdictions give a courtesy notice the day or two before the eviction, others do not, but the end result is the sheriff overseeing the landlord's movers removing all of the tenant's possessions from the property and placing them on the curb, and the tenants are forcibly removed from the property. At that point, the landlord can change the locks and the tenant can no longer return (They have been "evicted").
You can get help finding a new place to live by contacting your County Housing Authority. Let them know that you are facing a lease termination/eviction (emphasize that you are being displaced, not evicted for cause) by your landlord and they can place you higher on the priority list.