It will not be very easy especially if you pled guilty. Voluntary intoxication is not a defense so that will not help you but I am glad you want to get on the right track and move forward with you life. Good Luck!
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Very simply, in Ohio, sex crimes can not be expunged because there are enhanced penalties if you do it again so the state needs the prior crime record. Also, since so many years have passed, there is no way to vacate a plea if indeed you pled to the charge (you don't state how the conviction was obtained). I am sorry I could not be more encouraging.