Neosho Falls is a city in Woodson County, Kansas, United States. As of the 2020 census, the population of the city was 134. Neosho Falls wa…Neosho Falls is a city in Woodson County, Kansas, United States. As of the 2020 census, the population of the city was 134. Neosho Falls was founded in 1857, making it the oldest town and first county seat in Woodson County. It was named from the Neosho River, on which it is situated. The first post office in Neosho Falls was established in May 1857.