Odelein played junior hockey for the Moose Jaw Warriors before being drafted by the Montreal Canadiens in the seventh round (141st overall) in 1986.

His first NHL goal was a highlight-reel end-to-end rush against Chicago Blackhawks goalie Ed Belfour on December 19, 1991.

Odelein's tenure with the Coyotes was short as he was claimed in the expansion draft by the Columbus Blue Jackets on June 23, 2000.

The Panthers' general manager Rick Dudley expressed interest in retaining Odelein[1] when his contract expired, however, a lockout that erased the 2004-05 NHL season, and a changing of the guard in Florida that saw Dudley replaced by Mike Keenan, spelled the end of Odelein in Florida.

In March 2018, Odelein was hospitalized and diagnosed with critical illness polyneuropathy, after falling into a coma and suffering paralysis.

Odelein underwent a heart valve, liver, and kidney transplant at Allegheny General Hospital in Pennsylvania.