Abraham, John, and Henry "Henderson" in 1820 are definitely the Hardestys. They are living on school land leased by Abraham and John in 1819, just south of the land occupied by Henry Hardesty sometime between 1803 and 1807. This Henry Sr. is probably their father. There is no "Frederick Hardusty" in 1820--this is Frederick Henderson. The census taker made a lot of errors like this.
Henry Sr. appears to be living in 1820 on land owned by and adjacent to Ralph Hardesty, and Henry Jr. later lived on land in Salt Creek Township also owned by Ralph. I believe that Ralph is the oldest son of Henry Sr. Ralph's daughter Eliza (m. Robert Denny) noted her father as having been born in Maryland on the 1880 census. He is definitely not a son of Richard of Belmont Co. as has been reported. That Richard had three sons only: Robert, Samuel, and John.
Could the Henry who married Mary "Wattron" (probably Watson) in 1815 be Henry Sr., and Mary a widow? A William W. Watson b. 1812 appears to be very close to the Hardesty family and is buried next to Abraham's family in Ark Springs Cemetery, Meigs Township. Could he be Mary's son?
In 1804, a Henry Hardesty purchased land in Smith Township, Belmont County (R4 T6 S35) just south of McMahon's Creek, about six miles or so due west from Obediah Hardesty. I can't find any other records of him in Belmont County except for a tax list in 1808. Ruth Hardesty (b. 1782 in MD) married James Wilson/Willson in Belmont County in either 1802 (family record) or 1805 (History of Belmont County). Ruth was the sister of Abraham Hardesty, and thus probably Henry Sr.'s daughter. Ralph Hardesty married Obediah Hardesty's daughter Rebecca (b. 1779 according to tombstone in Hardesty Cemetery, Union Twp., Muskingum Co.) in Belmont County around the same time.
A Jane Hardesty (b. 1791 MD) married John West in Morgan Co. Ohio in 1820. Is this another daughter of Henry Sr.? Ruth Hardesty Wilson named a daughter Jane. Interestingly, on the 1776 census of Prince George's Co. MD, in the same area as the Hardestys, Jane Letman, 46, is living with John, 27, and two other females, 17 and 15. Could this be Ann Letman's mother? Henry m. Ann in 1777. Her name has been transcribed as Letman and Selman.
According to their placement on the census, John, Henry, and Joshua Hardesty of Patuxent Hundred, Anne Arundel MD, 1790, lived near the Hardestys (Robert, Alice Brown Hardesty Duvall, Edmond who d. before 1776) of Prince George's Co. (the Hyattsville area). Is this the Henry who married Ann and went to Muskingum County?