Oliver graduated from St. John's College in New York. He moved to Michigan and worked as a pharmacist. When the Civil War began he joined the 4th Michigan Volunteer Infantry Regiment as a private. He rose to captain in that regiment before being appointed colonel of the 15th Michigan on March 13, 1862. He led his regiment at Shiloh and commanded the 2nd Brigade, 6th Division during the siege and battle of Corinth. He returned to command the 15th Michigan during the siege of Vicksburg where he was part of the XVI Corps. He briefly commanded the 2nd Brigade, 4th Division, XV Corps and was transferred to Chattanooga in the wake of Ulysses Grant's victory there in 1863. Oliver was back in command of his regiment during William T. Sherman's preparations for the advance against Atlanta, but once the campaign got underway Oliver was in command of the 3rd Brigade, 4th Division, XV Corps. He briefly led the 1st Brigade, 4th Division at the battle of Jonesborough. During the March to the Sea, Oliver commanded the 3rd Brigade, 2nd Division, XV Corps. His was one of the brigades that assaulted Fort McAllister in December. On January 12, 1865 he was promoted to brigadier general of volunteers. He was at the battle of Bentonville, though his brigade did not see much action. He received a brevet promotion to major general of volunteers on March 13, 1865 and was in command of the 2nd Division, XV Corps at the close of the war. He was mustered out of the volunteer service on August 24, 1865.