The Oilers also got a fourth-round draft choice in 2011.
Sabourin had a 6-8-2 record with a 2.85 goals-against average in 19 games for the Penguins this season.
Garon's record with Edmonton was 6-8-0 with a 3.17 goals-against average.
"Addressing our goaltending situation was a high priority for us and moving forward, we believe we've accomplished that as well as acquiring some valuable assets for our organization," Oilers General Manager Steve Tambellini said.
Garon has played in 200 games with Montreal, Los Angeles and Edmonton. Sabourin has been in 57 contests with Calgary, Vancouver and Pittsburgh.
Stone has one assist in eight games in the NHL.