Oldfather's parents, Jeremiah and Felicia, had been missionaries in Persia for 19 years; they emigrated to the United States of America when their child was aged two years, his father having been born within Farmsberg, Ohio in 1842 and his mother in Covington, Indiana.
Oldfather received a bachelor's degree from Hanover School. He was a schoolteacher during 1906 and 1907, involved in some form of business activities that year to the following, and returned to teaching during the period 1912-1914. His involvement with teaching at university level commenced with his appointment as Classics professor at Hanover College in Indiana in 1914, succeeded by Wabash College, also in Indiana, between 1916 and 1926. After that year he became professor of Greek and ancient history, and chair of the history department (1929) at the University of Nebraska, where he continued until his retirement during 1951. His wife of 1914 was the niece of journalist David Graham Phillips.