U.S. Highway 2 runs roughly diagonally throughout Solway Township, in a northwest–southeast direction.

Morris Thomas Road (County 56) runs east–west through the southern portion of the township.

Canosia Road (County 98) runs north–south through the middle of Solway Township.

The White Pine River and Hay Creek both flow through Solway Township.

Saint Louis River Road runs east–west along Solway Township's southern boundary line with adjacent Thomson Township of Carlton County.

15.2% of all households were made up of individuals, and 5.5% had someone living alone who was 65 years of age or older.