Oliver was born around 1837 in Indiana, and then served in the 82nd Indiana Volunteers in the Civil War. He enlisted in August of 1862 and was only in the service a few months before he died in November. With the help of someone else researching, they had some more details about his death:
So I knew that he died of Typhoid in a field hospital in Bowling Green, Kentucky. I assumed that he was buried there in Kentucky. Well, turns out I was right. He was buried there initially, but then was re-interred in the Nashville National Cemetery. This cemetery was established in 1867. Then in 1869 they published a list of names of the interred and where they came from. Here is a caption from the introduction of the document:
The total number of dead interred in the cemetery is sixteen thousand four hundred and eighty-six, of which twelve thousand four hundred and eighty-seven are known, and three thousand nine hundred and ninety-nine unknown. Of white soldiers there are fourteen thousand five hundred and seventy-seven, and of colored one thousand nine hun dred and nine. The number of regiments represented is seven hundred and thirty, and of States and independent organizations thirty-one.
The bodies interred in this cemetery have been gathered from an extensive region of country, along the Cumberland River from Carthage on the east to Clarksville on the west; from the line of the Louisville and Nashville and Northwestern railroad to the Tennessee River at John sonville; from the Edgefield and Kentucky and the Memphis branch of the Louisville and Nashville railroad; from Bowling Green to Clarksville; from the Nashville and Chattanooga railroad to Lavergne; and from all intermediate and adjacent country; from the Nashville battle-field, and many of the skirmish grounds in Southern Kentucky, comprising those originally collected and buried at Tompkinsville.
The bodies interred in this cemetery have been gathered from an extensive region of country, along the Cumberland River from Carthage on the east to Clarksville on the west; from the line of the Louisville and Nashville and Northwestern railroad to the Tennessee River at John sonville; from the Edgefield and Kentucky and the Memphis branch of the Louisville and Nashville railroad; from Bowling Green to Clarksville; from the Nashville and Chattanooga railroad to Lavergne; and from all intermediate and adjacent country; from the Nashville battle-field, and many of the skirmish grounds in Southern Kentucky, comprising those originally collected and buried at Tompkinsville.
So in that honor roll listing I was able to find Oliver. The top image has the categories, but you can find Oliver [Orill] on the lower page.