High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Salem Township is one of the twenty-five townships of Muskingum County, Ohio, United States. The 2000 census found 830 people in the township, 703 of whom lived in the unincorporated portions of the township. It is one of fourteen Salem Townships statewide. The township is governed by a three-member board of trustees, who are elected in November of odd-numbered years to a four-year term beginning on the following January 1.