Uwa Elderson Echiejile had given the Super Eagles a fifth-minute lead, albeit in fortunate circumstances as his shot took a double deflection before sailing past goalkeeper Xavier Samin.
Oduamadi got his first of the night on 16 minutes, capitalising on a poor pass before slotting past the goalie.
It got worse for the Tahitians just before the half-hour mark when Samin failed to hold onto Ahmed Musa’s tame cross, allowing Oduamadi to tap home.
The African champions had a succession of chances to extend their lead but were wasteful in front of goal as they went into the break 3-0 up.
Tahiti then stunned with their first ever goal at a senior FIFA tournament – Jonathan Tehau rising highest at the back-post to head past Vincent Enyeama, playing in his 81st international.
However, the underdogs’ joy was short-lived when the self-same Tehau put a cross from Oduamadi past his own keeper.
And Oduamadi’s night was to get even better when he completed his hat-trick on 77 minutes; in the process becoming only the second player after Fernando Torres in 2009 to score three goals in one match at the Confederations Cup.
Echiejile put the icing on the cake with a sixth goal ten minutes from time, but coach Stephen Keshi will be concerned by the profligacy in front of goal, as well as some slack moments at the back.
Nigeria next face Uruguay, while Tahiti’s task gets even tougher as they take on world champions Spain.