There are 5 US Post Offices in Adair County serving a total of 23,666 residents equating to 4,733 residents per post office. It's estimated that approximately 37,774 packages are handled across the 5 county post offices annually. Adair County is a county located in the U.S. state of Oklahoma. As of the 2010 census, the population was 22,286. Its county seat is Stilwell. Adair County was named after the Adair family of the Cherokee tribe. One source says that the county was specifically named for Watt Adair, one of the first Cherokees to settle in the area.