Nashport is an unincorporated community and Census-designated place in western Licking Township, Muskingum County, Ohio, United States.Nashport was founded in 1827, and named for Captain Thomas Nash.[3] A post office called Nashport has been in operation since 1834.Built by Tami Longaberger, former CEO of The Longaberger Company, Eschman Meadows is ostensibly the largest home in the state of Ohio.This Muskingum County, Ohio state location article is a stub.