Oliver was a right-handed batsman who fielded primarily as a wicket-keeper. Oliver made his debut for Devon in the 1967 Minor Counties Championship against Cornwall. From 1967 to 1985, he represented the county in 43 Championship matches, the last of which came against Buckinghamshire.
He made his MCCA Knockout Trophy debut for the county in 1983 against Buckinghamshire.
From 1983 to 1986, he represented the county in 4 Trophy matches, the last of which came against Cornwall. Oliver also played List A cricket for Devon at a time when they were permitted to take part in the domestic one-day competition, making his debut in that format against Leicestershire in the 1983 National Westminster Trophy.
He played 2 further List A matches against Sussex in the 1984 National Westminster Trophy and Warwickshire in the 1985 National Westminster Trophy. In his 3 List A matches, he scored 55 runs in three unbeaten innings, with a high score of 33*.