He played college football at Central Arkansas before signing with the Indianapolis Colts as an undrafted free agent in 2018.

[1] As a senior, he was an All-Region selection at defensive back and punt returner and participated in the 2012 Tennessee vs. Kentucky National Guard and AutoZone Liberty Bowl All-Star Games.

[3] Odum was signed by the Indianapolis Colts as an undrafted free agent on May 1, 2018, and made the team out of training camp.

[7] Odum recorded his first career interception by picking off a pass from Dallas Cowboys quarterback Dak Prescott in a 23–0 win on December 16, 2018.

[8] In his rookie season, Odum played in all 16 games for the Colts (two starts) with 36 total tackles, including one for loss, an interception and two passes defended.

[9] Odum made one start during the season against the Kansas City Chiefs, making six tackles and forcing a fumble in a 19–13 victory.