In 1946, Oswald taught plant pathology as an assistant professor at the Davis Campus of the University of California. He was chairman plant pathology department at the Berkeley Campus in 1954. In 1962 he became vice president for administration in the statewide system for the University of California.
Oswald was president of the University of Kentucky from 1963 to 1968. He was executive vice president of the University of California from 1968 to 1970. In 1970, he became president of Pennsylvania State University until he retired in 1983. He died in Philadelphia, Pennsylvania in 1995.