In The Adventures of Ichabod and Mr. Toad, Brom Bones sings a jazzy song about the Headless Horseman to scare Ichabod. Brom is voiced by Bing Crosby, who also narrates the segment.
The Corpse Bride's "Remains of the Day" is a jazz song performed by Skeletal Musicians, and naturally contains creepy xylophone parts. While the skeletons are not villainous, the song provides the backstory for the titular Corpse Bride and tells of how she was murdered.
While it being jazz isn't notable in itself (the film has a jazz-influenced soundtrack), Dr. Facilier's Villain Song In The Princess and the Frog: "Friends on the Other Side" is unique. The tempo, minor key, and call-and-response elements make the song much creepier than other songs from the film. What's more, the song seems to be bit of a tribute to Minnie the Moocher, another case of this trope. Facilier looks a bit like Cab Calloway, and the weird dancing and Disney Acid Sequence aspects are reminiscent of some of the old cartoons.
Oogie Boogie from The Nightmare Before Christmas has loud, jazzy music for both his Leitmotif and his Villain Song. This signifies quite a few things about him, such as his love of gambling and his Boisterous Bruiser Scary Black Man personality. But most importantly, the contrast between his jazz music and the rather somber orchestral music associated with the other citizens of Halloween Town highlights how different he is from them — namely, how much more violent he is.