Elliott, 27, who had been in the midst of his first season with the Penguins organization, has appeared in 20 games for Pittsburgh's AHL affiliate, the Wilkes-Barre/Scranton Penguins, and has recorded eight points (one goal, seven assists) and four penalty minutes.
The Vancouver native was selected 49th overall by Colorado in the 2009 National Hockey League draft.
Lindberg, a 23-year-old Stockholm native, returns to the Senators after originally being selected 102nd overall by Ottawa in the 2013 draft.
Lindberg was traded to Toronto as part of the February 2016 trade that sent defenceman Dion Phaneuf to the Senators. The 22-year-old played six games for the Leafs and 66 for the Marlies over two seasons. He has nine points, all assists, in 17 games with AHL Belleville. He has spent almost all of his pro career in the AHL, save for six games with NHL Maple Leafs two years ago.
The Penguins acquire Sexton, a 27-year-old Ottawa native, who played in two games with the Senators last season, and Erkamps, a 23-year-old undrafted defenceman who now plays in the ECHL with the Brampton Beast.
In a separate deal, Ryan Scarfo, who was also skating in Brampton, was traded to the Penguins for future considerations.