From the Touring Ohio site.
Probably the reason I wasn't able to find out much about a Fort Greenville in Ohio was because it was called Greene Ville and was classified as an encampment.
It was built by General Anthony Wayne, 5 miles north of Fort Jefferson at what is now Greenville, Ohio. It had ten feet high walls and enclosed about 50 acres. It is said that it was the largest wooden fortification ever built.
It was named for Wayne's friend, Nathaniel Greene and laid out like a city.