The Beatles, I would claim, are primarily a "yeah" band. Witness "She loves you, yeah, yeah, yeah," and "Beep beep, beep beep, yeah!" (from "Drive My Car"). "Polythene Pam" has a "yeah, yeah, yeah!" or two as well. And most of the song "It Won't Be Long" is composed of nothing but "yeah." ("It won't be long, yeah, YEAH!, yeah, YEAH!, yeah, YEAH! It won't be long, yeah," etc.) However, a claim could be made that they are also something of a "hey" band, as heard in, for instance, "I Should've Known Better": "And I do, hey hey hey, and I do!"
The Stone Roses, perhaps, are also a "hey" band. See "The Hardest Thing in the World": "It never happens that way, a-hey hey hey, a-hey hey hey." Many hair bands from the '80s and '90s are "hey" bands as well. Def Leppard comes to mind: "You and me, babe, hey hey!" (That was from "Pour Some Sugar on Me," and I am proud to say I wasn't sure of that and had to look it up on the web.)
The Cure, meanwhile, is mostly a "do" band. Robert Smith, when he isn't just wailing mournfully in the lyric-free spaces, can often be found singing "do-do-do-do-do." Just listen to the end of "Friday I'm in Love," or the middle of "High."
David Bowie, in his elegant simplicity, tends to be an "oh" artist. For instance, "Oh-oh-oh-ohhh, little China girl," or "Didn't know what time it was, the lights were low-oh-oh, I leaned back on my radio-oh-oh" ("Starman"). But he does throw in some good "yeah"s in "Ziggy Stardust."
Morrissey may be the only one I can think of who is a "la-de-da" artist. ("I'm going to meet the one I love, la-de-da, la-de-da...") And Frank Sinatra, famously, of course, is a "do-be-do" artist.
Perhaps a separate species should collect what we might call "directive to lead guitarist" singers, who, just before the guitar solo, actually say something to the guitarist encouraging him or her to go ahead. Very common in cheesy '80s fare, e.g., Bret Michaels of Poison, in "Talk Dirty to Me": "C.C., pick up that guitar, and-a, TALK to me!" But also can be found from as far back as the '60s: Mike Nesmith of the Monkees in "Papa Gene's Blues": "Play, magic fingers!"
Suggestions for further taxa or specimens, o scientists of music?
P.S. Satire Alert Sticker: I'm basically joking and this is whimsical. I understand this would not be a good way to reorganize your CD collection.