One way to play on the existing superhero is to take the superpowers which are common to the superhero role and subvert them, creating a hero with a seemingly useless power: Invisible Spleen Man or the Skulk, who shrinks and becomes incredibly mild-mannered whenever he's angry. If you are using these heroes within a narrative, try constructing elaborate scenarios where the apparently useless power becomes invaluable. Alternatively, create a world in which the superhero is feared by his foes and loved by the public because of this "incredible" power though the hero himself is bemused or even frightened by the fact that the power has no obvious use.
Monty Python created the sketch "Bicycle Repair Man" in which the world is inhabited by supermen who idolize the mild mannered and unique Bicycle Repair Man. You can work out any number of examples of this formula; the IT technician or administrative assistant in a world of frustrated heroes who can't organize themselves enough to save anybody. The idea of a double identity can be just as effectively inverted, with the character playing an average super hero by day but the world-saving janitor by night.
Create a superhero spoof which uses a political or historical figure and parodies their character by describing the attribute which they are famous for in the manner of a comic book hero. Possible examples might include super Henry David Thoreau, capable of feeling alone in the wilderness at the end of any medium to large sized garden and live in the wild using only his wits and meals cooked by his mother, or super King Canute, who not only has no influence over the tide but has no influence on any meteorological or geo-environmental phenomena whatsoever.
Batman uses the motif and humanized abilities of bat to fight crime. He flies like a bat, moves without sound and in some instances uses echolocation to navigate in the dark. Try creating superheroes who borrow the attributes of much less suitable animals. Imagine Aye-Aye man, who can drum one incredibly long finger on walls to find hollow cavities, though he usually only finds grubs and woodworm, or Stork Man, who can stand on one leg for extended time periods and is exceptionally good at explaining where babies come from to young children.