The village is one of the homes of Laura Ingalls Wilder, author of the Little House on the Prairie books. Grace Ingalls, the youngest of the Ingalls children, was born there in 1877. There is a Laura Ingalls Wilder Museum in the local Masters Hotel.
Hamlin Garland, noted American novelist, poet, essayist, short story writer, Georgist, and psychical researcher lived on a farm in Hesper Township, near Burr Oak during the 1870s.
As of the census[7] of 2010, there were 166 people, 70 households, and 43 families residing in the town. The population density was 240.6 inhabitants per square mile (92.9/km2). There were 80 housing units at an average density of 115.9 per square mile (44.7/km2). The racial makeup of the town was 97.0% White, 0.6% Asian, and 2.4% from other races. Hispanic or Latino of any race were 2.4% of the population.
There were 70 households, out of which 31.4% had children under the age of 18 living with them, 52.9% were married couples living together, 8.6% had a female householder with no husband present, and 38.6% were non-families. 31.4% of all households were made up of individuals, and 11.4% had someone living alone who was 65 years of age or older. The average household size was 2.37 and the average family size was 3.05.
In the city the population was spread out, with 24.1% under the age of 18, 10.7% from 18 to 24, 22.8% from 25 to 44, 28.8% from 45 to 64, and 13.3% who were 65 years of age or older. The median age was 39.2 years. The gender makeup of the city was 52.4% male and 47.6% female.
Previously Burr Oak was within the North Winneshiek Community School District.[10] The school building was 3 miles (4.8 km) from Burr Oak.[11] North Winneshiek CSD operated all grade levels until 2001, when it ended its high school program. According to district agreements, students in the district could attend Decorah High or the high school program of Mabel-Canton Public Schools in Mabel, Minnesota.[12] Effective July 1, 2018 the North Winneshiek district consolidated into the Decorah district.[13] North Winneshiek School closed its doors at that time.[14]
In 2018 the combined interim board of Decorah CSD and North Winneshiek CSD approved an agreement with Mabel-Canton schools, effective for five years, to allow students in the former North Winneshiek district boundary to attend Mabel-Canton if they choose.[15] The agreement applies to any post-merger Decorah CSD resident who is geographically closer to Mabel than to Decorah.[16]