Born in Raleigh, North Carolina,[2] Odunze moved to England as a child and played for local youth teams before spending time in the Chelsea academy.[3][4] He moved to Canada when he was eleven and played for local sides Calgary Villains and Calgary Blizzard SC.[2] During this time, he went on trial with Welsh side Cardiff City, training with the first team despite only being fourteen.[2][5] In January 2019, he joined the Vancouver Whitecaps Academy from Calgary Foothills.[4] Later in the same year, Odunze signed with English side Leicester City.[6] He went on to train with the senior squad.[7]
Odunze signed with the Charlotte FC first team on January 18, 2024. His Major League Soccer contract is guaranteed through 2027 with a club option for 2028.[9]
Odunze is eligible for the United States, England, Canada, and Nigeria. He was called up to the Canada under-15 side in 2017 but has represented the United States at under-17 and under-20 levels.[10] He represented the United States at the 2019 FIFA U-17 World Cup, playing in two group-stage games.[2]