[3] For millennia the Great Plains of North America were inhabited by nomadic Native Americans.

The town was named for John B. Elwood, a pioneer settler.

[6] According to the United States Census Bureau, the city has a total area of 3.20 square miles (8.29 km2), all land.

[7] Elwood is part of the St. Joseph, MO–KS Metropolitan Statistical Area.

The 2020 United States census counted 1,125 people, 441 households, and 282 families in Elwood.

There were 494 housing units at an average density of 169.8 per square mile (65.5/km2).

29.0% of households consisted of individuals and 13.2% had someone living alone who was 65 years of age or older.

There were 533 housing units at an average density of 166.6 per square mile (64.3/km2).

28.9% of all households were made up of individuals, and 10% had someone living alone who was 65 years of age or older.

There were 494 housing units at an average density of 242.9 per square mile (93.8/km2).

25.8% of all households were made up of individuals, and 10.8% had someone living alone who was 65 years of age or older.

The community is served by Riverside USD 114 public school district.