Born in Catonsville, Maryland, Onderdonk was the father of Robert Julian Onderdonk and Eleanor Rogers Onderdonk. After receiving an academic education at the College of St. James, Catonsville, Onderdonk entered the National Academy of Design about 1872, where he studied two years under Lemual Everett Wilmarth. Onderdonk then enrolled in the Art Students League of New York, which he helped organize in 1875 along with William Henry Huddle and Henry Arthur McArdle, receiving instruction from Walter Shirlaw, James Carroll Beckwith, and, in his final year, from William Merritt Chase. Onderdonk also studied under Alexander Helwig Wyant while painting and sketching in and around New York City. Onderdonk traveled to San Antonio in 1878 to visit a friend. Finding the city congenial, he remained to make a precarious living teaching and selling his paintings. In 1889 he moved to Dallas in hopes of better prospects. The following year, he painted several portraits for the Hulburt Portrait Company, and in 1893 accepted the offer of a salaried position with the newly formed Art Students League of Dallas. Onderdonk illustrated The Life of John Wesley Hardin, from the Original Manuscript, as Written by Himself (Seguin: Smith and Moore, 1896), published the same year Onderdonk returned to San Antonio following the death of his father-in-law. Onderdonk resided, taught and painted in San Antonio the rest of his life save for a brief sojourn in St. Louis in 1898 – 1899. Onderdonk died in San Antonio.