Clinton is a city in Custer and Washita counties in the U.S. state of Oklahoma. The population was 8,521 at the time of the 2020 census…Clinton is a city in Custer and Washita counties in the U.S. state of Oklahoma. The population was 8,521 at the time of the 2020 census. The community began in 1899 when two men, J.L. Avant and E.E. Blake, decided to locate a town in the Washita River Valley.