Woodside Township was organized in 1877, and named for tracts of woods within its borders.

[3] According to the United States Census Bureau, the township has a total area of 36.2 square miles (93.8 km2), all land.

The racial makeup of the township was 96.59% White, 2.05% Native American, and 1.37% from two or more races.

13.3% of all households were made up of individuals, and 4.4% had someone living alone who was 65 years of age or older.

About 17.3% of families and 19.6% of the population were below the poverty line, including 19.3% of those under the age of eighteen and 25.9% of those 65 or over.