Oduya's fourth goal this season gave New Jersey a 3-1 advantage at 18:20 of the second period.
Parise's 28th (unassisted) upped New Jersey's lead to 4-1 at 2:05 of the 2:05 of the third.
Martin's fourth goal this season started the scoring at 11:52 of the first period.
Travis Zajac and Patrik Elias (empty net) also scored once each, while goaltender Scott Clemmensen was credited with 26 saves on 28 shots for the Devils, who head into the All-Star break with a five-game winning streak.
Montreal got one goal apiece from Josh Gorges and Matt D'Agostini (power play).
Goalie Carey Price was beaten four times on 33 shots in the Canadiens' second straight loss.
On the power play, the Devils went 0-for-2 and the Canadiens went 1-for-5.