Okay, in one sentence that's probably more lit-theory words than a guy with a biology degree should be allowed to use in a day (even on the internet) but indulge me, dear reader...
"Weird" we sometimes think of as a genre, as in "weird fiction" or "the weird tale" (or Weird Tales). HP Lovecraft adopted the term from Sheridan le Fanu, and defines it in his essay "Supernatural Horror in Literature":
As ST Joshi points out--and as a review of weird fiction reveals--weird can pervade several different traditional genres: horror (of a couple of different stripes), fantasy, ghost stories, and science fiction. A related form is the French literary genre of fantastique which is about supernatural incursion into realist narrative.
I think this gets at the key to weird. It's about things which are unnatural (or perhaps suggest a radically different interpretation of nature). The occurrence of these events is often transgressive or surreal. They can be used to evoke horror, or unreality, or decadence --maybe all three--depending on the context. I think this is perhaps succinctly analogized by one of the character's in Machen's "The White People": "...how awful it is. If the roses and the lilies suddenly sang on this coming morning..."
Weird is the Garden of Adompha, the city of Xuthal, the Horla, and The King in Yellow. It's also the Gray Caps, fungoid overlords of Jeff VanderMeer's Ambergris, and the red-curtained room with the oddly speaking dwarf in Twin Peaks.
Wonder hasn't been identified as cleanly in the literature as weird. It really comes into its own in film where visual effects (special and otherwise) combine with calculated musical selection to push us in its direction.
Wonder is Lothlórien, Shai-Hulud, and "My God--its full of stars!" It's Jack Kirby's New Gods, Avatar's flying mountains, and Gaiman's Dream confronting Lucifer Morningstar in Hell.
While weird evokes the paranormal and "negative" qualities, wonder evokes the transcendent and "positive" qualities.
An interesting question, I think, is can these sensations be evoked in gaming?
Certainly, I feel like weird can. I think since the earliest days of the hobby, adventure writers and creature designers have groped for it. The blogosphere is full of efforts to bring it to bear, many successfully. I think its more than a matter of aping nineteenth century gothic lit, or 1930s pulp fiction, though. Some of those elements are too familiar. Borrowing of ideas from newer sources like fiction of the New Weird, the films of David Lynch, or some foreign horror films (euro- or j-) will probably do the trick. Kenneth Hite's works on gamemastering horror would also probably prove instructive.
Wonder is a bit tougher. Without visuals, it hinges on appropriate description--which is tough to do off the cuff and without knowing where the audiences' heads are going to be at the moment the description is delivered. The comic book approach of "mad ideas" where there's less focus on the centerpiece scene, and more on a flood of the "impossible" (or at least the kind of trippy) to create a similar effect. If you can't describe the city in overview in such a way that your player's are in awe, you can whittle them down with a lot of "smaller" amazing things as they're coming into town. The risk, of course, is in overdoing it, and making the interesting things too common-place.