Rodriguez was on the provisional roster for Spain, Amezaga for Mexico and Moylan for Australia. Rodriguez, the first player from last year's Draft to reach the big leagues, is on the Major League roster; Amezaga and Moylan are non-roster invitees.
Dodgers still planning to compete are shortstop Hanley Ramirez (Dominican Republic), first baseman Adrian Gonzalez (Mexico), third baseman Luis Cruz (Mexico), infielder Nick Punto (Italy) and right-handed reliever Ronald Belisario (Venezuela).
Players could miss up to three weeks of Spring Training, as World Baseball Classic games begin March 2, with the final March 19.
Although free agent J.P. Howell was signed to be the situational lefty with Scott Elbert recovering from elbow surgery, Rodriguez made an impact last September and he could force his way back into the big league bullpen this spring.
"This is my first Spring Training with the team," said Rodriguez, whose parents were born in Cuba but became citizens of Spain. "I want to stay here and get used to everything. I wanted to participate, but I felt I needed to stay."
Amezaga will be hard pressed to make the Opening Day lineup, but could be an early callup because of his versatility to play all over the field.
"Sometimes in situations, you have to think what's best for you," said Amezaga, who might have started in center field for Team Mexico. "It's best for me to stay here so they can see me and I can prove that I'm healthy."
Amezaga has had a series of knee injuries and was with the Dodgers in 2010, only to miss the entire season following microfracture knee surgery.
Moylan, an effective setup man with Atlanta when he wasn't battling elbow, back and shoulder problems, is contending for a relief spot.
"I'm with a new team and I wanted the organization to know that I was committed," said Moylan. "As much as I'd love to play for Australia, I'm really looking to establish myself here. Had I still been with [his original club, thre Braves], it wouldn't have been an issue."