Fergie Jenkins pitched 402 innings with an ERA+ of 122 and was traded for John Poloni and cash. There's one. Bill Lee is obviously another. The Cecil Cooper (for the back end of the careers of Bernie Carbo and George Scott) trade has always looked odd to me. Anyone else?
Looking at the list of players on the 1976 Sox that were no longer with the team a couple of years later, you have:
Denny Doyle: Released after the 1977 season after putting up an OPS+ of 55; the Sox had just acquired Jerry Remy. Out of baseball after that.
Rick Miller: Left as free agent after the 1977 season. He came back 3 years later as part of the Burleson/Hobson trade, so probably unrelated.
Rico Petrocelli: Released after the 1976 season during which he had an OPS+ of 67 at the age of 33.
Steve Dillard: Utility infielder traded to the Tigers after the 1977 season for a pair of minor league players.
Doug Griffin: Released in 1977 after appearing in only 5 games. Never played again; IIRC, he had lingering affects of a concussion resulting from a Nolan Ryan fastball.
Bobby Darwin: 34 y/o journeyman utility player traded to the Cubs for bullpen flotsam (Ramon Hernandez).
Bob Heise: Another journeyman, sold to the Royals the following offseason.
Deron Johnson: Yet another journeyman player. Released in June of 1976 at the age of 37, and out of baseball after that.
Luis Tiant: Left as free agent after 1978 season.
Rick Wise: Traded for Dennis Eckersley.
Rick Jones: Drafted by the Mariners in the 1977 expansion draft.
Jim Willoughby: Sold/dumped by Boston to the White Sox after a subpar (92 ERA+) year in 1977. Was 28, but played only one season with Chicago before being out of baseball for good.
Dick Pole: Claimed by the Mariners in the expansion draft.
Tom Murphy: Fungible reliever sold to the Blue Jays in 1977 at the age of 31.
Tom House: Sold to the Mariners in 1977.
Rick Krueger: Traded to Cleveland for Frank Duffy after the 1977 season.
Jenkins, Lee, Cooper, and Cleveland were already noted upthread; that Cecil Cooper trade really deserves to be near the top of all time bad trades by the Sox. Nearly all of the players above were at or close to the end of their careers. Steve Dillard is probably a candidate for the list: utility fielder, with decent stats for a UT at the time, dumped for a pair of minor league players at the age of 27. Willoughby was also dumped for nothing after 3 seasons of an ERA+ of 118, 141, and 92 with Boston. The other moves seem more the typical churn of the flotsam and jetsam of that time.