Eveland, 28, was arbitration-eligible for the first time and likely not to be tendered a contract next week after going 3-2 with an impressive 3.02 ERA in a late-season callup.
Despite those numbers, the Dodgers elected to add established free agents Harang and Chris Capuano in the past two weeks.
Martin, 22 and an 18th-round Draft pick, was 5-12 with a 4.96 ERA at Class A Delmarva with 97 strikeouts but 65 walks in 110 2/3 innings.
Henson, an outfielder who turns 24 next week, batted .247 with three homers and 36 RBIs in 123 games with Triple-A Norfolk last season.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.