The city was platted in 1909 by John James Welder and David Odem. It was named for Odem, who was the county sheriff. Odem is a city in San Patricio County, Texas, United States. The population was 2,499 at the 2000 census. According to the United States Census Bureau, the city has a total area of 1.1square miles (2.9 Square kilometers), all of it land.