When does Niv-Mizzet's trigger resolve?
In a 2-player game, you would lose the game and the Niv-Mizzet triggers would not resolve.
The Wheel of Fortune you played would resolve as the only object on the stack. After the Wheel has finished resolving, before the damage triggers would even be put on the stack, you would lose the game for having attempted to draw from an empty library.

116.3b The active player receives priority after a spell or ability (other than a mana ability) resolves.
116.5. Each time a player would get priority, the game first performs all applicable state-based actions as a single event (see rule 704, “State-Based Actions”), then repeats this process until no state-based actions are performed. Then triggered abilities are put on the stack
704.3. Whenever a player would get priority (see rule 116, “Timing and Priority”), the game checks for any of the listed conditions for state-based actions
704.5b If a player attempted to draw a card from a library with no cards in it since the last time state-based actions were checked, he or she loses the game.