From the maps I've seen on Poison Sumac (Toxicodendron vernix), it is in Ohio. Remember though that the plant likes swampy conditions and is not generally seen by most folks. A great site by the US government has maps for a great number of plants. I can't give you a direct link to the poison sumac page but if you go here:
USDA plants database
And then search for poison sumac either by common name or scientific name, you'll get a picture, map and some basic information.
I searched for Poison Oak and neither is listed to be in Ohio. You can do the same search to see where these plants are known to be.