Oliver earned second-team All-Pac-10 honors as a running back in the 1978 and 1979 seasons, and he was an honorable mention in 1980. His career total of 3,096 rushing yards was the second best in U of A history. He accounted for nearly a third of that total during the 1979 season, which included a performance of 196 yards in 25 carries against Colorado State. He was named Pac-10 Player of the Week after a 27-24 Wildcat victory over arch-rival Arizona State in 1979. Oliver was team captain during the 1980 season and played in the 1981 East-West All-Star game. He played pro ball with the NFL Philadelphia Eagles.