Strathcona is a city in Roseau County, Minnesota, United States. The population was 44 at the 2010 census. A post office called Strathcon…Strathcona is a city in Roseau County, Minnesota, United States. The population was 44 at the 2010 census. A post office called Strathcona has been in operation since 1905. The city was named for Donald Smith, 1st Baron Strathcona and Mount Royal.