No, movement does not happen simultaneously.
Unfortunately, overwhelming strike is written such that:
Hit: 1[W] + Wisdom modifier damage. You shift 1 square and slide the target 1 square into the space you occupied.
You initiate a shift. Because the shift does not state "even into the enemy's square" it follows the normal rules of a shift:
SHIFT: MOVE ACTION Movement: Move 1 square.
which follows the normal rules of movement, save for the not-provoking elements.
Creatures occupy squares. Given that there are specific powers, (King's Castle, Rogue Encounter 1: Effect: Switch places with a willing adjacent ally.) which state "switch places", the general "slide 1" is not overridden by the "and slide enemy into the space you occupied."