Oliver was elected to the Iowa House of Representatives of the Tenth Iowa General Assembly in 1863, to represent the district composed of the counties of Carroll, Crawford, Monona and Sac.[2] He was a delegate to the Republican National Convention in 1864.[1] He became a prominent member of the Iowa House, and at the close of his term was elected to the Iowa Senate for the Forty-fifth District, composed of fifteen counties in the northwestern part of the State, serving from 1865 to 1867.[1] He was then chosen as circuit judge, and was twice re-elected, serving from 1868 to 1875.
Oliver was mayor of Onawa several times. He became one of the most extensive farmers in western Iowa after retiring from public life.[2] Addison and Hannah Oliver had ten children, one of whom, Cyrus G. Oliver, became a member of the Iowa General Assembly.[3] He died in Onawa, and was interred in Onawa Cemetery.[1]