Sheary, 27, has 19 points in 55 games this season. The 26-year-old Rodrigues has nine points in 38 games.
The deal sees Sheary go back to Pittsburgh, where he spent the first three seasons of his career. He was traded to Buffalo in the 2018 off-season.
Kahun, 25, collected 27 points across 50 games in Pittsburgh. He was acquired from the Chicago Blackhawks as part of the Olli Maatta deal last summer.