Terms of the deals were not disclosed.
Beauvillier had 15 goals and 13 assists in 47 games last season in what was his fifth NHL campaign.
Cizikas, who made his NHL debut in 2011-12, had seven goals and seven assists in 56 games.
Palmieri joined the Islanders at the trade deadline last season and had nine points in 19 playoff games.
Sorokin made his NHL debut last season, playing in 22 games. He had a 13-6-3 record with a 2.17 goals-against average and a .918 save percentage.