Usually, Carl and Sheen are the only two people in town who Jimmy trusts with his secrets and getting into his lab. He also sometimes uses them to test his dangerous experiments, which Carl hates but Sheen enjoys. They also hang out with Jimmy because they get bored and lonely without him (they have no lives).
Sometimes though, they refuse to cooperate with Jimmy and make him pretty irritable, due to their hijinks and complete incompetence. In some cases, they pressure Jimmy into his making dangerous things or force him into doing things he really doesn't want to do, which cause the problem of the episode. Jimmy sometimes can be unsympathetic to their feelings though.
Carl may not be as smart as Jimmy, but he is very loyal to him. He's willing to help Jimmy as much as possible, but hates testing Jimmy's inventions. Normally, he plays the foils to Jimmy's genius and sometimes solve the episode's crisis with some innocent or insane observation. However, other times, he is the cause of the problem. He accompanies Jimmy in his wild adventures and usually ends up in trouble. Jimmy likes Carl because he is loyal and helps Jimmy with his experiments.
Sheen is always showing off his new action figures to Jimmy and talking about them, which Jimmy doesn't seem to mind. Sheen is responsible for a great deal of the blunders Jimmy often has to fix. He also volunteers to test Jimmy's experiments, but not nearly as often as Carl. Like Carl, he is not near as smart as Jimmy. Jimmy likes Sheen because he is hyperactive, even though Sheen can be insensitive to Jimmy and Carl's feelings.
In Sheen's Brain, when Sheen becomes an evil genius and gains reality warping powers, Jimmy and Carl prove their loyalty to him by trying to change him back to normal before his head explodes, even though Sheen keeps torturing them with his new powers. Finally, Sheen brutally strikes Jimmy and Carl with a lightning bolt after they try one last time. When he sees Jimmy and Carl and believes them to be dead, he realizes his new powers have turned him into a monster and changes back to normal right before the exploding can occur. When Jimmy and Carl are revealed to be alive, Sheen apologizes to them for what he did. This proves how loyal the three are to each other.