Elihu is kind of a creeper. Seriously—look at the facts. He isn't mentioned as one of Job's friends, but apparently he was there listening in on their conversation, because he knows all about it when he chimes in. And then he takes it upon himself to spend about five chapters—an eighth of the entire book—spouting off his thoughts.
Other than his long speech, Elihu is never mentioned. Theorists just eat this stuff up because it helps them decide what was written down when. The more a story arc makes sense, the more likely it is that the whole thing was written down at the same time. Since things are a bit random in Job—like, for instance, Elihu's magic appearing and disappearing act—scholars aren't so sure. Maybe it was put in at a different time.
Elihu's brief appearance does more than just help tweed-sporting scholars make estimations about dates. It also opens up the text to new theoretical possibilities. After all, he basically comes in, says his bit, and then heads out, leaving it up to us to interpret his words.
What are his words? Like Job's so-called friends, Elihu claims that God has power beyond man. But he kind of stands up for Job, too. The ways of God are mysterious to man—just think weather patterns—so who's to say Job is guilty? Maybe he's innocent but being punished anyway. His point: Job should stop obsessing about justice: "But you are obsessed with the case of the wicked;/ judgement and justice seize you" (36:17). When it comes down to it, Job is asking the wrong questions of God.
Elihu is a tricky guy, too. His speech uses material and language from the other speeches that we heard first. It's an old rhetorical trick: quote your opponent and use his own material against him. Job is the perfect target for this because his speeches pose questions. Elihu, in 35:1-4, quotes Job, and then says, "I will answer you," before making his point. Pretty fancy.
Are we supposed to trust this guy? Probably. The fact that he hasn't said anything until now makes him a better arguer, right? He has listened to everyone else, and now he says his bit.
Up until this point, Job's three friends have been shoving it down our throats that Job messed up. Elihu backs it up a bit. He basically says, "who are we to say what God is doing?" And because we know what's going on up in the heavens—ah, dramatic irony—we're pretty sure that Elihu is right.