O’Donnell was born in Norwalk, Connecticut, and moved to Jackson, Michigan, with his parents in 1848.
During the Civil War, he enlisted as a private in the First Regiment, Michigan Volunteer Infantry, and served two years.
He was appointed in 1878 aide-de-camp on the staff of Governor Charles Croswell, with the rank of colonel.
In 1892, he ran in Michigan's 2nd congressional district, losing to Democrat James S. Gorman.
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