The Nats recalled Dukes and purchased the contract of Sosa after Friday night's 5-4 loss to the Pittsburgh Pirates.
Dukes and Sosa will fill the roster spots of first baseman Nick Johnson and reliever Joe Beimel, who were traded on Friday.
"We think Elijah's ready to come back up here and help us," Nationals interim manager Jim Riggelman said. "We're glad to have him back, and we're looking forward to seeing Sosa pitch. We've heard some good things about him. Hopefully, those two guys can help us get this thing going right."
Formerly one of the game's top prospects when he was with the Tampa Bay Rays system, Dukes hit only .190 with 10 home runs and 21 RBIs in 184 at-bats with the Nationals earlier this season.
A career .237 hitter in 190 big-league games, the 25-year-old Dukes was batting .288 with three home runs, 10 RBIs and five steals in 68 at-bats for Triple-A Syracuse.
"[Dukes] has been swinging the bat very well, and he's been working on a lot of the things we asked him to work on," Washington interim general manager Mike Rizzo said. "He's been great down there... and now he gets a chance to come up here and play."
Sosa, 32, was 1-2 with a 2.79 ERA and three saves for Syracuse. A veteran of 254 major league games with four teams, he had allowed only two earned runs in his past 10 appearances.
"Sosa's been throwing the ball extremely well, and that's why we brought him up in lieu of a couple other guys," Rizzo said. "Of anyone on that staff, he was by far the manager and pitching coach's choice to be called up to the big leagues."