By writing in third person, Steinbeck is able to manipulate your feelings as a reader so you feel what he wants you to feel. He's able to convey all of the fear, lonliness, pride, etc. of all of the characters. This is why a reader is able to feel optomistic about the possibility of buying the dream ranch in one chapter, scared for Lenny in another, and sympathetic to George in another.
Now, think about how that would change if it were written in first person from any of the characters views. Are you able to feel bad for Candy and his dog if you're inside George's mind? Are you able to be scared for Lenny if you're inside Curley's mind?
Steinbeck was a master of characterization in all of his novels. Writing in third person was a large part of this. It would have been more difficult to get you to connect to every character as well if OMAM had been written in first person.