Landlord wants me out , 30-day Notice to Vacate and says can move out any time, can I move early w/o penalty?

My lease expires on July 31 and my landlord has put a "30-day notice to vacate". And in that he also says that I'm "currently on a month-to-month basis" and "he would like to have the possession of the property on or before July 31st,2010". I'm confused because I'm not on month to month (its June and lease ends july31!). Since he says I can move before the end of my lease (July 31) can I move out June 30 to new apartment without a problem (will i be able to legally get my security deposit back if i do this)? (Could I just quit at 11th month without legal problems?) Btw I'm in 'OH'