Most Greek gods had great strength, but none of them was particularly in charge of this quality.
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Cratus is the Greek god of strength.
Cratus was the god of strength, might, power and sovereign rule.
Bia was the spirit (daimona) of force, power, might, bodily strength and compulsion.Site; http://www.theoi.com/Daimon/Bia.html
As most Greek gods are, well, gods, yes they have "superhuman" powers, including strength. To a Greek god or goddess, moving a mountain isn't hard.
His name was Antaeus, the son of Poseidon and Gaia.