What happens when opponent draws Exodia and Deck Out in the same turn?
The deck out is irrelevant. The player drawing Exodia (and presumably completing the set in hand) has already won the duel.

Even if the player has not completed Exodia in hand, they do not lose until they are required to draw and are unable to draw. They may sit with an empty deck until next draw phase if there is nothing else to cause the duel to end.