Oak Run is a small an unincorporated community and census-designated place 23 miles east of Redding in Shasta County, California, United States. Its population is 158 as of the 2020 census. It has a store and a post office run by a family who lives in the town-famous "Oak Run House", just behind the store and post office. It also has a church, school, libr…Oak Run is a small an unincorporated community and census-designated place 23 miles east of Redding in Shasta County, California, United States. Its population is 158 as of the 2020 census. It has a store and a post office run by a family who lives in the town-famous "Oak Run House", just behind the store and post office. It also has a church, school, library, a volunteer fire department and 765 people. The ZIP Code is 96069. The community is inside area code 530. It was the site of a massacre of 300 Yana Indians in 1864