In the State of Ohio is it true the tenant has to give 30 days notice when they are moving out and the landord has to give 30 days notice when asking them to move out? If they do not give 30 days do they lose their security deposit?

On a month to month lease the rule is generally that notice of one full rental period is necessary for temination by either party. So if the rental period is a calendar month, you can't give 30 days on 7/15 and terminate on 8/15.

A security deposit is used to secure against damage to the property. It MAY be used for unpaid rental in many states. But its not automatically forfeited if insufficient notice is given.

Yes, a calender month notice is normal notice The people renting are expect to pay for this notice, if they fail to do so, the money can be held out of the deposit.