Dillon Falls is an unincorporated community in Muskingum County, in the U.S. state of Ohio.Dillon Falls was named for Moses Dillon, who settled here at the falls of the Licking River.[2] A post office called Dillon was established in 1887, and remained in operation until 1908.[3] Besides the post office, Dillon Falls had a station on the Baltimore and Ohio Railroad.This Muskingum County, Ohio state location article is a stub.