Austwell is a city in northeastern Refugio County, Texas, United States. Its population was 147 at the 2010 census. Austwell was laid out in 191…Austwell is a city in northeastern Refugio County, Texas, United States. Its population was 147 at the 2010 census. Austwell was laid out in 1911. The city's name is an amalgamation of Austin and McDowell, the names of its founders Preston R. Austin and Jesse C. McDowell.