St. Denis agreed to terms on a two-year, two-way contract with the Islanders on Tuesday.
Halak finished a poor season with a 3.19 GAA and .908 save percentage.
Soderstrom is expected to make his professional debut with Bridgeport of the AHL next season, Newsday reports.
Beauvillier was a solid contributor on the second-line for the Islanders this season with 21 goals, 15 assists, and a plus-2 rating.
Eberle enjoyed a solid first season with the Islanders as he tallied 25 goals, 34 assists, and was a plus-5 in 81 games.
Wagner was less than impressive with the Islanders as he only had one goal and zero assists in 15 games since being acquired at the trade deadline.
Mayfield finished the season with two goals, ten assists, and a minus-6 rating in 47 games for the Islanders.
Davidson had a goal, assist, and was a minus-8 in 15 games for the Islanders this past season.
Johnston finished the 2017-18 season with three goals, three assists, and 62 penalty minutes in 24 games.
Tavares could still be traded by the Islanders before the NHL draft, Newsday reports.
Quenneville made his professional debut in AHL Bridgeport's 5-2 loss to Lehigh Valley on Friday.
Lee finished the 2017-18 season with 40 goals and 22 points for the Islanders.
Pelech had three goals, 16 assists, and a plus-seven rating in his first full NHL season.
Nelson finished the 2017-18 season by getting at least one point in four of his last six games.
De Haan (shoulder) has confirmed that he will be ready for next season's training camp, Brian Compton of NHL.com reports.
Kulemin (shoulder) told reporters he would have been ready for the playoffs if the Islanders had qualified, Andrew Gross of Newsday reports.
Quine stated Sunday that he is fully healthy after missing the last 28 games of the season due to "nagging injuries", Andrew Gross of Newsday reports.
Fritz was reassigned to AHL Bridgeport on Sunday, Andrew Gross of Newsday reports.
Pulock scored a power-play goal and added an assist during Saturday's 4-3 overtime win against Detroit.
Barzal recorded two assists -- one on the power play -- during Saturday's 4-3 overtime win against the Red Wings.
Fritz (illness) is active for Saturday's game against the Red Wings.
Quenneville signed a three-year, entry-level contract with the Islanders on Friday, Arthur Staple of The Athletic New York reports.
Fritz will not play in Thursday's game against the Rangers due to illness.
Tavares scored twice -- once on the power play -- during Tuesday's 5-4 win over Philadelphia.
Eberle recorded two assists during Tuesday's 5-4 win over Philadelphia.