Benjamin Digby Odlum, Texas Revolution veteran and member of the Republic of Texas Congress, was born in County Kildare, Ireland, about 1807 and at an early age moved to New York. He arrived in the McMullen-McGloin colony in 1834 and in 1835 received a third of a league that later became part of McMullen County. At that time Odlum described himself as a carpenter. He joined the command of James W. Fannin, Jr., command on March 1, 1836, and was with Amon B. King's command when it was captured on March 15 in the battle of Refugio. Odlum was spared from execution in the Goliad Massacre. He apparently escaped, but surrendered to Gen. José de Urrea at Victoria and was used by the Mexican army as a laborer. Subsequently he either escaped again or was released; he was discharged from the Texas service on October 31, 1836. In 1838–39 Odlum represented San Patricio County in the House of the Third Congress. At one time he was president of the San Patricio County Board of Land Commissioners.
He married Mary Anne O'Connor on September 8, 1838, in Victoria, and they had two children. After his marriage, Odlum received two-thirds of a league and one labor from the Victoria County Board of Land Commissioners. In 1839 he received a bounty warrant for 640 acres for his participation in the battle of Refugio. Mrs. Odlum died in 1848 and was buried in San Patricio. By 1850 Odlum had moved to Houston and was working as a wheelwright. In the census that year he reported real estate valued at $2,000.
His daughter, Elizabeth Anne, married Richard W. Dowling, who led the Confederate troops at the battle of Sabine Pass. Odlum's son was killed in Confederate service in Louisiana. Odlum was a Catholic. He died in Houston on January 9 or 10, 1861.