The date you close and they give you the money IS the date the new owners take possession. If you bought a car would you pay the money and then let the seller drive it around for the next month? If you needed to stay you should have told your agent and they would have written it into the contract or you could have delayed the closing until you were ready to move. You can't have it both ways - you can't take the money and stay in the house too.

I am not familiar with the real estate laws in OH, as I am an agent in Minnesota, however when it comes to real estate it is always important to get it in writting. In MN your agent would have built that into your purchase agreement. This is necessary since the property changes hands at time of closing unless otherwise detailed in the purchase agreement.

It is sad to say this but 8 of 10 people don't know how to be accountable to their word anymore so it will always protect yourself to get something so important in writting. You may want to try to make an arrangement with them for the remaining time, but may need to offer some consideration ($$) for the time at the house. Be sure to get that in writting as well, even a hand written note that is signed by you and the new owners should work to prevent continued headache over this.

if there is nothing in writing and they now own the house,they can force you to move at any time,although i imagine they would have to go through a formal eviction process.

Wow. I cannot even imagine a contract that did not specify the possession date. Given the situation is what it is now, I would ask for something in writing so that the agreement is clear.