Yes, according to the Ohio Bureau of Motor Vehicles (BMV) you can drive out of state with your learner's permit, abiding by your restrictions, particularly that you have a valid licensed driver, the age of 21 or over, in the front passenger seat with you.
Also if you have a learner's permit from another state it is legal to drive in Ohio. You may operate a vehicle in the state of Ohio with a valid learner's permit from another state, as long as there is a valid licensed driver, the age of 21 or over, in the front passenger seat.
If you have an OH learner's permit and want to drive out of state then be sure to contact the states in which you plan to visit. Check with their Department of Motor Vehicles (DMV) to make sure it is legal for you to operate a car there with your Ohio. If you can drive in other states be sure to also ask the DMVs what restrictions or conditions you will have on you.
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Since you asked specifically about West Virginia we found out what their stance was on out of state learner permits. The West Virginia Division of Motor Vehicles said they will honor any driver's license or learner's permit for operation in their state. The learner's permit or driver's license must be valid and must adhere to all restrictions mandated by the issuing state.
So if you have a permit from Ohio you may drive in WV as long as you comply with all of the rules and regulations of your OH permit. You should also check with your insurance provider to make sure whatever car you are driving in WV will cover you driving.
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