Oliver graduated from Florida with a bachelor's degree in criminal justice in 1989, and was inducted into the University of Florida Athletic Hall of Fame as a "Gator Great" in 2000. In one of a series of articles written for The Gainesville Sun in 2006, the Sun sports editors chose him as No. 24 among the greatest 100 Gators from the first century of Florida football.
Oliver was selected by the Miami Dolphins in the first round (twenty-fifth overall) of the 1989 NFL Draft, and played seven seasons for the Dolphins (1989–1993, 1995–1996) and one season for the Cincinnati Bengals (1994). Oliver was reunited in the Dolphins' defensive backfield with his former Gators teammate Jarvis Williams, and the pair were the Dolphins' starting safeties for the next five seasons. Arguably Oliver's greatest career highlight was an October 4, 1992 interception of a pass thrown by Buffalo BillsquarterbackJim Kelly, which he returned 103 yards for a touchdown, and is the longest interception return in Dolphins history.
During his eight-year NFL career, Oliver played in 117 regular season games, started 101 of them, and recorded 544 tackles and twenty-seven interceptions, two of which he returned for touchdowns.
Following his professional football career, Oliver used his pro sports connections to launch a business as a professional party liaison for sports stars and celebrities in South Florida. When his party connections began to dry up, he focused on the real estate market to become a specialist in high-end, up-market properties for celebrities, and is currently a general partner in a Miami-based real estate firm.