Afton's power is unknown.
the aftons are not real
Stefan doesn't have a power!
She was born with it.
Laurent does not possess a special vampire ability in the Twilight Saga.
Heidi's power is to create illusions of someone's desires.
no, not so far but maybe in eclipse (the next twilight movie)
if I'm correct, none.
Ben.
James had the power of tracking. He could follow any scent.
hearing people's thoughts.
In the story they never reveal what Heidi's power is but she does have one.
Corin's power is said to be Paralytic Venom which is where you can spit venom from a distance to paralyse the target, but I think it will say so in the Twilight Saga Official illustrated guide. :)