Oden was the son of Alexander and Elvira Sims Oden of Talladega County. Alexander died at the age of 22 shortly after Edley was born. Elvira subsequently married William Peyton Hickman of Trussville, who later served as Jefferson County Treasurer.
Oden served as a young Confederate private in the Civil War and was remembered for taking "an active part in restoring this government to the rule of the white men in Alabama during the days of reconstruction."
Oden married the former Martha Ware in Birmingham in May 1872. He was awarded a homestead patent in Trussville in 1881. By 1891 he was working as a sales representative for John E. Ellis & Co. wholesale and retail druggists.
In 1898 Oden and his son James were partners in the opening of the Alabama Distilling Company, which built an $11,000 still on the banks of Five Mile Creek near East Lake. The distillery was raided by revenue agents that November, but resumed operations after civil penalties were paid. James "Spoon" Motlow joined the venture as an investor in 1901. Oden later filed a lawsuit arguing that his partner J. L. Lockwood had failed to satisfy thousands of dollars in debt to him.
Oden later resided at Village Springs. Martha died in 1899 and he was remarried, to the former Bernia Cozby, daughter of Commissioner J. E. Cozby of Remlap in December 1906. He stood as a candidate for Blount County Sheriff in 1914.
Oden died in 1930. He was survived by his second wife and by seven children and several grandchildren. His funeral was held at his daughter's home in Woodlawn and he was buried at Oak Hill Cemetery in Birmingham.
- "E. J. Oden Rites" (November 13, 1930) The Birmingham News, p. 25
- "Edley J. Oden Dead" (November 20, 1930) The Southern Democrat, p. 1
- Edley Oden at Findagrave.com