An injury to Brian Elliott effectively sent St. Louis on a search for late-season help between the pipes. Nilsson can provide the team with support behind Jake Allen.
Nilsson appeared in 26 games with the Oilers this season, posting a 3.14 goals-against average and a .901 save percentage.
Elliott was placed on injured reserve earlier this week with a lower-body injury. He will be re-evaluated in four weeks.
Lundstrom, a 23-year-old native of Varmdo, Sweden, appeared in 13 games with the Elmira Jackal of the ECHL and four games with the Chicago Wolves of the American Hockey League.
In a corresponding move, the Oilers have recalled goaltender Laurent Brossoit from the AHL's Bakersfield Condors.