Obvious qualities: Oz is fairly laid back, as noted with the “I’m not really a computer person. Or a work of any kind person.” He also expresses very little emotion, and I think it’d be easy to get the laid-back attitude and emotional inexpressiveness confused, but it’s fairly clear that they’re not the same thing. He’s quite capable of feeling emotion, as evidenced by the end of “Lover’s Walk” through the reconciliation in “Amends.” He just doesn’t say much about it.
He’s also highly intelligent, although the show downplays this somewhat with his slacker persona. One of the reasons he and Willow make such a great pair is that they’re both so incredibly geeky and brainy, although in really different ways -- she tends to be very practical and hands-on, wanting to do stuff on the computer or with magic, while he’s interested in abstract concepts (typified by the existential ponderings that Buffy overhears in “Earshot”). And when he gets into an intense situation, his method of recovery is repeatedly (well, twice -- after “Lover’s Walk” and “Wild at Heart”) to withdraw and think about things until he can sort them out. His choice after “Wild at Heart” to take off on a really long road trip is so Oz -- not only is he looking for a way of dealing with the wolf, but he’s processing the recent events and his part in them in the way most comfortable to him : he goes off alone and he thinks until things makes sense. Of course, this turns out to bite him in the butt.
(It strikes me that Oz/Cordy would make a really interesting couple. He sees everything and doesn’t talk about any of it; she’s not particularly perceptive, but she says exactly what she thinks. Again, contrast their thoughts in “Earshot”.)
(Another side note: how did brainy Cordy ever put up with Harmony? Are fashion accessories really so powerful a unifier?)
As I’ve been rewatching S2 and the beginning of S4, it’s struck me that a lot of what Oz says could just as easily come from Xander. His cultural references are similar; he has the same tendency to derive humor from weird juxtapositions of concepts (although I suppose that’s really more a Buffyverse thing than the trademark of any particular character). But their deliveries are totally different. Xander always comes off a bit as though he’s at a comedy club. He has set-up and a punchline, and if you cut him off in the middle you’d miss all the humor (other than the humor of watching him get cut off). Xander’s a performer. Oz isn’t, not in the sense I mean, even though he’s the one who actually gets paid to perform. Oz says something, and if you stopped him right there you’d have a complete thought. Oz is also much less self-conscious than Xander, while also, I think, being more self-aware -- is that possible? Self-aware but not self-conscious? Here we go: Xander is always conscious of how he appears to other people (or how he thinks he appears to people), but Oz pretty much just doesn’t care. I think this is the crux of that ‘coolness’ conversation they have in “The Zeppo.” Oz is cool partly because he doesn’t care about being cool. I have difficulty imagining Xander ever having the “I mock you wiz my monkey pants” conversation. Oz is just much more comfortable with himself than Xander.
Another difference: Xander uses sarcasm. Oz doesn’t -- at least I don’t think of it as sarcasm. When he says, “On the plus side, you killed the bench, which was looking shifty,” that’s not sarcasm so much as sheer absurdity. He uses irony, yes; sarcasm, no. (And now I’m trying to figure out how I’m differentiating those two, and not doing a very good job. Sarcasm has a, I dunno, a bite to it, a value judgment. I can’t decide if sarcasm is partly in the delivery, or if you can tell them apart by the words alone.)
Oz is also extremely level-headed. He’s darn near unflappable -- see his comments when informed vampires are real. He functions really well in dangerous situations, or in situations that’d be stressful to most people. (Willow: “How can you be so calm?” Oz: “Many arduous hours of practice.”) If he’s ever been afraid of an external situation, he hasn’t shown it.
And, Oz has pretty much the single best approach to relationships of anyone in the Buffyverse (with the possible exception of Riley in S4). He won’t kiss Willow the first time she asks him because he says it’s for the wrong reasons; he refuses to sleep with her the first time she offers, for the same reason. He forgives her after the Xander-kissing incident.
In fact, Oz appears to be so internally secure (minus some possible philosophical angst) that it makes sense his downfall comes, in some sense, from an external source. He doesn’t choose his wolfiness, and I think it terrifies him to suddenly be completely out of control when he’s used to being so very in control of himself (nice contrast, now that I think about it). Of course, the writers then did nothing with this for a season and a half (except for that one time when Xander fell asleep, in “Beauty and the Beasts”).