Burr Oak, OhioBurr Oak is an unincorporated community in Athens County, Ohio, United States. Burr Oak is located on Ohio State Route 13, north-northeast of Glouster. Burr Oak State Park is within walking distance and is named after the community.HistoryA post office called Burr Oak was established in 1887, and remained in operation until 1911. The community was named for burr oak trees near the original town site.