A journeyman backup, McElhinney has seen limited work this season behind all-star Sergei Bobrovsky.
The 33-year-old has gone 2-1-2 with a .924 save percentage and 2.39 goals-against average.
Columbus recalled prospect Anton Forsberg, 24, from Cleveland Monday to take over the backup role. Forsberg has shone in the AHL, going 12-6-1 with a .930 save percentage.
Bobrovsky (ill) was ruled out Tuesday, so the the Jackets also called up Joonas Korpisalo on a temporary basis.
Snatching the London-born McElhinney is a low-risk move for Toronto, which is leaning heavily on No. 1 goalie Frederik Andersen.
McElhinney turns UFA on July 1 and carries a modest $800,000 cap hit.
The Oilers’ chance on the 32-year-old Gustavsson, who posted a winning record with Boston in 2015-16, has not panned out.
The Monster has started five of the Oilers’ 42 games, posting a dismal 1-3-1 record and a save percentage of .878.
Edmonton is expected to call up Laurent Brossoit, 23, from Bakersfield to support No. 1 netminder Cam Talbot.
The 25-year-old scored just one goal and registered five points in 18 appearances with the Hurricanes this season. He’s only squeezed into the lineup twice since Dec. 10, and his demotion to Charlotte likely means forward Elias Lindholm, out of the lineup with an upper-body injury since Dec. 31, is returning to action.
In other waiver news, Buffalo Sabres centre Derek Grant was placed on waivers Tuesday. He has no goals and three assists in 35 games this season.