You owe income tax in the state where your permanent residence is located (Ohio) on all your world-wide income, including income produced in other states.
You owe state income tax in West Virginia only on WV-source income (the gas wells). You should be filing a WV non-resident income tax return that only taxes the gas well income. Then, you claim a credit on your Ohio tax return for the tax you paid to WV, which will partially or completely offset the WV income tax you paid.
RITA is your Ohio city taxes. Not every Ohio city that levies an income tax is part of RITA, but many are. Unfortunately, you owe income tax to your Ohio city of permanent residence on all your world-wide income, no matter where it was earned. That's how you pay for city services and so on where you live.
