Engel combined to hit .259 with seven home runs, 46 RBIs, 90 runs and 45 steals over 129 games between Class A Winston-Salem, Double-A Birmingham and Charlotte last season.
Goldberg was 3-5 with a 2.70 ERA and 10 saves in 47 relief appearances between Birmingham and Charlotte.
May, limited by injury to 83 games, batted .266 with 19 steals for Charlotte.
The White Sox also outrighted minor league pitcher Brandon Brennan to Charlotte on Friday.
Chicago's 40-man roster is at 40.