Because of the reciprocity between OH and PA, you will get a full refund of the OH state tax withheld, when you file the OH non resident return. Ask your OH employer to not do OH state withholding.
The reciprocity agreement does not apply city income tax, you cannot get the box 19 (of your W-2) amount refunded. If you are subject to a PA local income, you could check to see if they allow a credit for other city tax paid.