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.
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Most Greek gods had great strength, but none of them was particularly in charge of this quality.
Most of the gods in Greek mythology originated from the ancient Greek civilization.
Though there are many features of the Greek gods, I would say that a main one is their immortality.
Zeus and hades
Athena and hermes