Very simple forms, and sing-song, singable melodies. Kitschy stride patterns. Percussive, repetitive patterns. Physicality. Humor.
Intellectual eccentricity. Harmonic complications. Dissonances. Weird vacillations.
So complexity and simplicity. It's cerebral on one level but deeply moving, with emotional depth and a variety of other emotions, humor, tenderness, melancholy.
The melodic gift is undeniable. That is primary, with distinctive approaches, as well to harmony, rhythm, and timbre. A lot of original compositions by jazz players, well, they are not melodically distinctive. You wouldn't remember them. I saw on you tube part of a concert, and the leader announced that they would play an original composition called ... and then they proceeded to play "Sophisticated Lady" with a disguised melody.