[2] Oswayo is a Native American name purported to mean "the place of flies".

As of the census[5] of 2000, there were 251 people, 91 households, and 67 families residing in the township.

There were 91 households, out of which 33.0% had children under the age of 18 living with them, 61.5% were married couples living together, 7.7% had a female householder with no husband present, and 25.3% were non-families.

19.8% of all households were made up of individuals, and 11.0% had someone living alone who was 65 years of age or older.

About 10.6% of families and 20.2% of the population were below the poverty line, including 27.7% of those under the age of 18 and 21.2% of those 65 or over.