He attended Houston County Elementary School and graduated from Rushford High School in Rushford, Minnesota. He studied law at the Union College of Law in Chicago.
He was admitted to the bar in 1878 and commenced practice in Lanesboro, Minnesota. Steenerson moved to Crookston Polk County, Minnesota in 1880. While serving in the state senate, Steenerson served on the committees for the Hospital for Insane, Indian Affairs, Joint University and University Lands, Judiciary and the State Prison.
Steenerson was elected as a Republican to the 58th, 59th, 60th, 61st, 62nd, 63rd, 64th, 65th, 66th, and 67th congresses, (March 4, 1903 – March 3, 1923).
He was chairman of the Committee on Militia (60th and 61st congresses) and served on the Committee on Post Office and Post Roads (66th and 67th congresses). Steenerson was an unsuccessful candidate for reelection in 1922 to the 68th congress.
He served as vice president of the American group of the Inter-Parliamentary Union. He resumed the practice of law in Crookston, Minnesota.
Steenerson died on November 22, 1926.
He is buried at the Oakdale Cemetery in Crookston, Polk County, Minnesota. Steenerson is the namesake of Steenerson Township, Beltrami County, Minnesota.
He served as prosecuting attorney of Polk County 1881 – 1883. As city attorney of Crookston. As a member of the Minnesota Senate 1883 – 1887.
And as delegate to the Republican National Conventions in 1884 and 1888.
Married Maria C. Fjaagesund, November 24, 1878.