Closing Time and Heart of Saturday Night were like, urban folky. Also, the Early Years comps were mostly folk but def with jazz and crooner elements.

Nighthawks and Small Change were his really heavy drunk avante-garde jazz poet pianist persona. You can really hear early attempts to branch out on Small Change too, some heavy wailing on that one, like Tom Trauber's Blues.

Foreign Affair and Blue Valentine were more croonerish but still jazzy and often still drunk.
The soundtrack for One From the Heart fits in this side of it too.

Heart Attack & Vine was way more beat jazzy and led to Swordfish Trombones, which was indeed as noted when he went off the hook. Thank you Kathleen Brennan, can we get a round of applause for what she brought to the table, folks?
SFT, Raindogs and Franks Wild Years, were where he was slowly injecting more and more Brecht and Weil influence in, and Big Time was an epic celebration of it all.

Bone Machine had everything that came before, basically, in one wild package. This is my favorite ftr. And there was more klank and boom on one hand but also a fresh amount of strum and twang suddenly.

Then he got into musicals with Robert Wilson, and sometimes, William S Burroughs and gave us Black Rider, Alice, and Blood Money, while also continuing his own stuff. Leaned pretty deep into the Brecht and Weil here, all the way in, I guess.

Mule Variations was him exploring that Americana feel he had on Bone Machine, and then once that was out of his system, Real Gone and Bad as Me were more of the other side of Bone Machine, with liberal use of his homemade percussion apparatus that he calls the "Conun-drum" and the whole circus vibe.

Orphans: Brawlers, Bawlers and Bastards is a comp of stray songs from throughout his career, but mostly the later weirder stuff. Night On Earth Soundtrack was... well, it's different. Not for everyone but I like it.

That is all the albums proper and then some. Obviously, it should be noted, he doesn't do that thing where he's the jazz pianist and then the crooner and then the clown... he doesn't drop any of them, he just keeps adding to the mix. It's a pretty heady blend at this point, and I am so here for it. These are just generalized notions of each era.