Of Mice and Men is told in third person omniscient, but the focus is definitely on George and Lennie. We know what they are thinking mostly because of what they say though. We are not inside any one character’s head, and there is no first person narration.
Most of the narration is like this:
The first man stopped short in the clearing, and the follower nearly
ran over him. He took off his hat and wiped the sweat-band with his
forefinger and snapped the moisture off. (ch 1, p. 2)
At this point, we don't know anything about the characters- not even their names. First they are described.
First person narration is most easily recognized by the use of I and my, and other first person pronouns. In a first person narrator, we are inside one person’s head and we know everything that one person is thinking, but only that one person. Although there is dialogue in the book where characters talk using the word I or my, dialogue is not part of the narration. Consider this dialogue by George.
George unslung his bindle and dropped it gently on the bank. "I ain't sure it's good water," he said. "Looks kinda scummy." (ch 1, p. 2)
If George was talking to the reader, it would be first person. Instead, he is talking to Lennie. So this is still third person.
The use of the third person omniscient means we can see every character equally. We remain objective, and we can only see the characters like we were watching a movie. This distances us from the action, because we only know what characters are thinking based on what they say.
The story is neither. The story is in third person limited because the author really only reveals George's thoughts except at the end you get inside Lennie's head a little bit when Steinbeck writes about the bunny and Aunt Clara.