The chorus of this song has a pretty simple harmonic vocabulary of diatonic chords (I, ii, IV, and V) plus one blue chord (bVII), but the melody is quite unusual. The fact that it sounds fairly natural is remarkable and somewhat mysterious.
The first two phrases revolve around D#, the third of the scale. It's an odd tone for everything to be centered around because it's not a part of the ii (C# minor), IV (E major), or V (F# major) chords that we are hearing.
The third phrase starts off on D# once again, but has to slip up a half-step to E when the A major chord is thrown in to avoid a tritone. E is a part of the A major chord, but the phrase goes up a pitch and then descends to B (a longer note on a strong beat), which is not.
The last phrase emphasizes D# on the downbeat once again over C# minor.