No. Whatever the power tells you do, that's what you do. Only with the default melee basic attack or a power gained from str-based class do you do +strength modifier.
So Iron Fist does 1w+Constitution. If you were using a Rapier and had an 18 Constitution(+4 modifier) and no other options, you'd do 1d8+4 damage unaugmented. If you augmented it by 2 points, you'd do 2d8+4 damage.
(edit: and the damage would be untyped, not psionic)