Jonah Hex was by all accounts human and did not possess any superhuman powers.
Jonah Hex was an expert bounty hunter and skilled in the ways of tracking and survival. Both in the Confederate army and with the Apaches he was trained in the use of firearms, sabre, bow, tomahawk, and hand-to-hand combat. He is widely considered the greatest bounty hunter to ever live in his lifetime. During his tenure in the 21st century, Jonah Hex developed automotive skills and expertise in using futuristic weaponry.
Hex is much stronger than the average man in his time, due to his fighting experience and harsh training that started as a child, and continued throughout adulthood.
Jonah once owned a horse named General. After General was killed by stray fire in Weird Western Tales (Volume 1) #22, Jonah made use of whatever horse was available to him at any given time.
Two ivory handled .44 caliber Colt dragoon pistols, one Bowie knife, lever action rifle, an 1860 Light cavalry sabreand other weapons germane to the 19th century American southwest. In the 21st century, Hex had access to a variety of futuristic firearms.