Vernon is located in Jennings County, the only such named county in the United States. The town is on the National Register of Historic Places and is the host of many firsts in the state. The first area set aside for use as a public playground in Indiana (The Commons) is located in Vernon. The first elevated railroad overpass west of the Allegany’s. The state’s first all women's jury and the first Disciples of Christ Church were in Vernon. It was also the home of Indiana's fourth state park, now called Muscatatuck County Park.
There were 117 households out of which 32.5% had children under the age of 18 living with them, 49.6% were married couples living together, 15.4% had a female householder with no husband present, and 31.6% were non-families. 27.4% of all households were made up of individuals and 14.5% had someone living alone who was 65 years of age or older. The average household size was 2.40 and the average family size was 2.83.
In the town the population was spread out with 20.9% under the age of 18, 11.5% from 18 to 24, 33.6% from 25 to 44, 19.7% from 45 to 64, and 14.2% who were 65 years of age or older. The median age was 35 years. For every 100 females there were 124.5 males. For every 100 females age 18 and over, there were 123.1 males.
The median income for a household in the town was $29,750, and the median income for a family was $36,875. Males had a median income of $28,333 versus $22,143 for females. The per capita income for the town was $17,367. About 5.2% of families and 9.5% of the population were below the poverty line, including 18.1% of those under age 18 and 4.3% of those age 65 or over.