The moves were the latest in a series by general manager Dean Lombardi to unload players before Tuesday's trade deadline as part of his efforts to rebuild the slumping Kings, who will not make the playoffs this season.
Norstrom, the Kings captain since 2002, is the team's career leader in games played among defencemen with 780. He has two goals, seven assists and 40 penalty minutes in 62 games this season.
"Mattias solidifies our defensive group and also adds character and veteran leadership to our locker-room," Stars general manager Doug Armstrong said. "We look for him to make an immediate impact on this hockey club as we push towards the playoffs."
In a separate trade, the Kings acquired defenceman Jamie Heward from the Washington Capitals for a conditional fifth-round pick in 2008.
Heward has four goals, 12 assists and 27 penalty minutes in 52 games.
Tuesday's deals were the Kings' fifth trades in a month. In January, Craig Conroy was shipped to Calgary for centre Jamie Lundmark along with a fourth-round draft pick in 2007 and a second-round pick in 2008. Earlier this month, Sean Avery went to the New York Rangers for Jason Ward, plus two prospects. On Monday, Brent Sopel was traded to Vancouver for conditional second-and fourth-round picks.
Modry will begin his second stint with the Kings, where he played from 1996-2004. He was an all-star with the team in 2002.
He has one goal, nine assists and 32 penalty minutes in 57 games with the Stars this season. He's also played for Atlanta, Ottawa and New Jersey during his 12-year NHL career.
The Kings also acquired the rights to Johan Fransson from the Stars. The 22-year-old defenceman has an assist and two penalty minutes in six games with Assat Pori of the Finnish League this season. He played 140 games for Lulea HF of the Swedish Elite League from 2002-06.
"Like with most trades, this was a very difficult decision to make," Lombardi said. "Matty has been a tremendous player for this club for a number of a years and he has been a very respected captain as well. The ability, however, to get two high draft picks will be of great benefit for our organization as we move forward and help build our reserve list and team."
Fransson was drafted in the second round by the Stars in the 2004 NHL entry draft. He played for Sweden in the 2005 and 2006 world junior championships.
Pushkarev has two goals, two assists and eight penalty minutes in 16 games with the Kings. The 22-year-old defenceman also has played in 35 games with Manchester of the AHL this season.
The Kings will get three draft picks from the Stars - a first-rounder in 2008, and picks in the second and third rounds in 2007.
Dallas will receive a third-and fourth-round picks in the 2007 draft from the Kings.