In a way, all of the characters are influential, as everyone's actions affect another in some fashion. This ripple effect is what Steinbeck deemed a "phalanx theory", that is, all parts work together to influence the whole. Some groups, like the phalanx of Curley's world, are warped and the phalanx itself reflects the trauma.
George and Lennie have the most influence on one another. Although Lennie is mentally impaired, he gives George a sense of purpose in that Lennie could not survive without him. Together, they influence each other by keeping their dream of living without the oversight of a boss, and "livin' off th' fatta the lan'" alive.
Curley is influential because it is he who dictates who will live comfortably and who will be miserable. His cronies, like Carlton and Slim, have less influence but under his direction, they too can make the lives of the hands good or bad.
The character who on some levels who has the least influence is Curley's wife. Notice that she has so little value in her group that she is not even given a name. Her influence on others is derived solely from her sexuality.
Candy is not influential because he is old and useless, much like his decrepit dog. He can no longer be a part of Slim's masculine team, and his lack of value makes his influence negligible.
Who is "influential" will depend on your interpretation; for good or ill, all characters affect others.
In Of Mice and Men, Whit is pretty insignificant in that he is only mentioned once or twice, but he plays no role in the drama that unfolds. The boss is also only mentioned, but again, plays no major role other than being the vehicle for his son's (Curley's) ability to boss the rest of the workers around. Lennie's Aunt Clara is mentioned (and she materializes in chapter six in Lennie's imagination), but she serves to function as the link between George and Lennie because she was the one to ask George to care for Lennie after her death.