Oden earned a PhD in engineering mechanics from Oklahoma State University in 1962.
He taught at OSU and The University of Alabama in Huntsville, where he was the head of the Department of Engineering Mechanics prior to going to Texas in 1973.
He has held visiting professor positions at other universities in the United States, England, and Brazil.
He was a Fellow and past President of both the American Academy of Mechanics and the Society of Engineering Science.
Oden was also elected a member of the U.S. National Academy of Engineering in 1988 for pioneering work in computational mechanics, which significantly advanced the transformation of nonlinear continuum mechanics into a powerful and widely used engineering tool.