As a defensive back, punt returner and outside linebacker at Central Arkansas, Odum's physicality on defense earned him the honor of becoming Southland Conference's Defensive Player of the Year in 2017.
Odum totaled 223 solo and 91 special teams career tackles, 29.0 tackles for loss, 6.5 sacks, 13 passes defensed, two interceptions (one returned for a touchdown), six forced fumbles, four fumble recoveries and three blocked kicks. He also registered three career punt returns, taking one all the way for a touchdown.
Odum joined the Indianapolis Colts in 2018 as an undrafted rookie. In four years with Indianapolis, Odum thrived as a key special teams player.
"Being in a smaller college, I had to put up a lot of stats," Odum said. "When I first got (to the NFL) it was smoke and mirrors … the game is more mental. I've improved my mental and everything else. Now, it's about concentrating more and learning my main tasks, seeing what I can improve on."
One of Odum's most productive seasons came in 2020 when he was named First-Team All-Pro and landed on the Pro Football Writers of America All-NFL Team. Odum played in all 16 games and caught the attention of the football world with a league-leading 21 special teams tackles. Since entering the NFL in 2018, Odum's 35 special teams stops are tied for the third-most in the league.
Odum earned a special teams Pro Football Focus grade of 91.0 in 2020. He was tied for the second-highest grade in the league among non-kickers on special teams.
"He is a tough kid," Colts special teams coach Bubba Ventrone said in 2020. "He's willing to do anything you ask him to do. He's very productive and instinctive. He does a good job. He just consistently finds the ball in all these coverage units and he's improved in the return game. He's been a great guy for our unit overall and obviously the production has been outstanding this year. To be able to lead the league in tackles at this point in the season is a testament to him and his hard work and his toughness."
In 2021, Odum played a larger role on defense, collecting a career-high 55 tackles, one forced fumble and one interception.
"I've always been a dog," Odum said. "I'm always going to hit, I'm never afraid of hitting. I'm never slowing down on point-of-contact."