He attended private schools, including Paulding Institute, and then became a partner in the mercantile business of Odell & Clark while also becoming involved in his father"s steamboat business on the North River.
Odell served in town offices, including Greenburgh town clerk and justice of the peace. He served in the New York State Assembly from 1857 to 1861. He established the First National Bank of Tarrytown and served as cashier from 1862 to 1864.
In 1866 Odell was elected Westchester County Treasurer.
He was reelected in 1869 and again in 1872. Odell was elected as a Democrat to the Forty-fourth Congress (March 4, 1875 – March 3, 1877).
He was not a candidate for renomination in 1876. After leaving Congress Odell resumed his banking interests and also became involved in the real estate business.
After having served for several years as assistant postmaster, from 1887 to 1892 and 1894 to 1898 he served as postmaster of Tarrytown.
Odell died in Tarrytown, New York, October 30, 1904. He was interred at Sleepy Hollow Cemetery in Sleepy Hollow, New New York