The Blue Jays sent right-hander Drew Hutchison, catcher Reese McGuire and outfielder Harold Ramirez to the Pirates.
In the deal for Feldman, Toronto shipped right-handed pitching prospect Guadalupe Chavez to the Astros. The Blue Jays shuffled veteran right-hander Jesse Chavez and cash considerations to the Dodgers for Bolsinger.
The 32-year-old Liriano is just 6-11 with a 5.46 ERA in 21 starts this season. He is 94-90 with a 4.09 career ERA in 11-plus seasons, topped by a 16-8 record with a 3.02 ERA and 162 strikeouts in 2013.
Feldman, 33, is 5-3 with a 2.90 ERA in 26 appearances (five starts) for the Astros this season. He is 69-76 with 4.35 ERA in 11-plus big-league campaigns.
Bolsinger, 28, made six starts for the Dodgers and went 1-4 with a 6.83 ERA. He is 8-16 with a 4.61 ERA in 37 major-league appearances (36 starts).
Hutchison won his lone decision in three games with Toronto in 2016 while posting a 6-5 mark with a 3.26 ERA in 18 starts with Triple-A Buffalo. The 25-year-old, who won a personal-best 13 games with the Blue Jays in 2015, owns a 30-21 career record with a 4.92 ERA in 76 major-league outings.
McGuire, 21, is batting .259 with one homer and 37 RBIs in 77 games with Double-A Altoona.
Ramirez, 21, is hitting .306 with two homers and 49 RBIs in 98 contests with Altoona.
Jesse Chavez went 1-2 with a 4.57 ERA in 39 appearances for the Blue Jays. He is 25-40 with a 4.55 ERA in 292 major-league games (49 starts).
Guadalupe Chavez, 18, was 4-1 with a 1.69 ERA in six starts for the Rookie-level Gulf Coast League Blue Jays.