Trinway is an unincorporated community and census-designated place in northern Cass Township, Muskingum County, Ohio, United States, in the east-central part of the state.The village is 52 miles east of the state capital of Columbus and near the town of Dresden.It was also the site of the first railroad station for the nearby village of Dresden.29.0% of all households were made up of individuals, and 26.1% had someone living alone who was 65 years of age or older.This Muskingum County, Ohio state location article is a stub.