Wedgewood, 26, appeared in 48 games with the AHL’s Rochester Americans in 2018-19, going 28-14-2 with a 2.68 goals-against average, a .908 save percentage and five shutouts.
Wedgewood has played 164 career AHL games with Rochester, Ontario and Binghamton/Albany, showing a record of 81-51-15 with a 2.47 GAA, a .908 save percentage and 13 shutouts.
In 24 career NHL contests with Arizona and New Jersey, Wedgewood is 7-10-5 with a 3.05 GAA, a .903 save percentage and two shutouts.
Wedgewood was originally selected by the Devils in the third round of the 2010 NHL Draft.
Martin, 24, appeared in 23 AHL games with the Colorado Eagles last season, going 9-10-2 with a 3.40 goals-against average, a .902 save percentage and three shutouts — including a 68-save effort at Ontario on Jan. 25.
Martin has played 125 games in the AHL over four seasons with Colorado and San Antonio, showing a record of 49-58-11 with a 3.02 GAA, a .903 save percentage and nine shutouts.
Selected by Colorado in the third round of the 2013 NHL Draft, Martin made his NHL debut with the Avalanche in 2016-17, making three appearances.
Mueller, 33, completed his 11th AHL season in 2018-19, scoring a career-best 33 goals and adding 32 assists for 65 points in 60 games with the Toronto Marlies.
Mueller was voted a Second Team AHL All-Star, the first postseason recognition of his career.
A two-time Calder Cup champion (2014, 2018), Mueller went on to post five goals and five assists for 10 points in 13 playoff games in 2019.
Mueller, a native of West Seneca, N.Y., has played 711 regular-season games in his AHL career, posting 222 goals and 305 assists for 527 points with Toronto, Tucson, San Diego, Hartford, Texas, Milwaukee, Lake Erie and Grand Rapids.
He has also notched 32 goals and 42 assists for 74 points in 101 Calder Cup Playoff games.