After graduation from high school in 1996, Odom enrolled at the University of Missouri and played linebacker for the Tigers, starting for four seasons.

[5] Odom helped guide Ada to a second straight state title,[3] in a 29–7 win over Clinton, that saw him run for 144 yards an 4 touchdowns.

[9] After Odom ran the 100-meter dash in 10.6 seconds, in the spring of his senior year, Larry Smith offered him a scholarship at the University of Missouri regardless of how his surgery went.

[10] Typically a 9-month recovery time for an ACL surgery, but Odom was able to be on the field again in three and a half months, participating in the Missouri fall preseason camp.

[10] In a game against Tulsa, Odom was named the Big 12 Conference Defensive Player of the Week collecting 8 total tackles and an interception.

With Odom and 1997's leading tackler, Harold Piersey returning in 1998, along with several of the starters on offense, the Tigers were expected to be one of the better teams in the Big 12.

[20] Odom was chosen as a team captain as a senior in 1999 and would go on to finish with 362 tackles — the fourth-most in school history at the conclusion of the 1999 season.

[23][24] Odom returned to Columbia, Missouri the following year, taking over as head football coach at Rock Bridge High School in February 2001.

[26] Six weeks after the season ended, Gary Pinkel hired Odom as a graduate assistant at Missouri.

Wanting to run a college program, Odom joined the Mizzou staff, first as an administrative graduate assistant for Gary Pinkel in 2003.

In that role, Odom oversaw coordination of the team's budget, travel plans (including bowl trips to the Sun, Cotton and Alamo bowls during that stretch), compliance issues, facilities operations and scheduling, as well as assisting with recruiting operations and managing the day-to-day overall operations of the program.vAs director of football operations, he coordinated all public relations activities and community service events that required the presence of Mizzou's football student-athletes, and also played a role as part of the design and planning team that oversaw the expansion and renovation of the Mizzou Athletics Training Complex, which opened in February 2008.

[33] During his three seasons as safeties coach, the Missouri Tigers went 26–13, including a 2010 Big 12 North division title.

[34] In 2012, Odom left Missouri to become defensive coordinator of the Memphis Tigers under head coach Justin Fuente.

[38] Odom's Tigers ranked ninth in the nation in total defense, allowing just 302.0 yards per game.

On September 3, 2016, Odom lost his first game as head coach of Missouri, a 26–11 road loss against West Virginia.

[43] The following month, Missouri lost five consecutive games and their 11-consecutive SEC game, culminating with a 31–21 defeat at the hands of South Carolina[44] He finished his first season as the Tigrers' head coach with a 4–8 record, with victories against Eastern Michigan, Delaware State, Vanderbilt,[45] and a redeeming victory in the Battle Line Rivalry over Arkansas, 28–24.

[47] In Odom's 2nd season, Missouri was picked to finish last in the seven-team Southeastern Conference Eastern Division by pre-season experts.

[62] Odom became the first Missouri coach to make a bowl game in his second year since Warren Powers did so in each of his first two seasons in 1978 and 1979.

On December 5, 2018, Missouri game Odom a contract extension, he had previously been the lowest-paid coach in the conference.

[81][82] Odom's raise paid him $3.05 million a year which ranked 11th among 14 head coaches in the SEC Conference.

[101] Before the team's final week, the NCAA announced that Missouri's appeal for their part in an academic scandal dating back to a 2016 whistleblowing.

[103] Odom was fired the next morning, citing a lack of momentum coming from the Tigers 5 game losing streak the section half of the season.

[104] On December 16, 2019, Odom was hired by new Arkansas Razorbacks head coach Sam Pittman as defensive coordinator.

[105] In March, 2020, it was announced that Odom would be given a pay raise to $1.3 million due to another undisclosed SEC team trying hire him.

Odom’s helped 2022's squad earn a bid to the Liberty Bowl, there was speculation of him leaving to become the head coach at Tulsa.

[124] In the following game, the Rebels defeated Air Force 31–27, taking sole possession of first place, and clinching a share of the Mountain West Title.

[126] UNLV finished the regular season 9-3 and earned the right to play Boise State in the Mountain West Conference Championship Game.

[135] During the bye week, starting quarterback Matthew Sluka announced on social media he would redshirt and not play in any of the Rebels' remaining games during the 2024 season.

[147] In the Fremont Cannon, the Rebels defeated Nevada 38–14, to clinch a spot in the Mountain West Conference Championship Game.

[151] On December 8, 2024, Purdue University announced Odom as the 38th head football coach in program history.