There is no way that PA will transfer money to OH to cover your taxes. Your employer no longer has the money, he is required to send it to PA promptly.
1. As soon as possible, you should file PA Rev-419 to stop the PA withholding. Your employer may, but is not required to, withhold OH income tax. If he doesn't, you may need to begin filing OH estimated taxes.http://www.revenue.pa.gov/FormsandPublications/FormsforBusinesses/Documents/Employer%20Withholding/r...
2. Prepare your federal income tax return.
3. Prepare a non-resident PA income tax return. If your only PA income is wages, you will only need the PA40 form and Schedule W2S, you can do this by hand and mail avoiding extra TT fees. hand: http://www.revenue.pa.gov/FormsandPublications/FormsforIndividuals/Pages/Personal%20Income%20Tax/Per...
From PA40 instructions :Resident of a Reciprocal State Filing for a Refund If you are a resident of a reciprocal state working in Pennsylvania and your employer withheld PA income tax, you may request a refund of the PA tax. You report zero taxable compensation on Line 1a, and the PA tax withheld on Line 13. You must submit a legible photocopy of your Form W-2, a copy of the resident income tax return that you filed with your resident state (without the supporting forms and schedules), and a statement explaining that you are a resident of a reciprocal state.
4. Lastly, prepare your OH income tax return, reporting all income including that earned in PA.
You will likely get a large refund from PA but owe quite a bit to OH.