If your mind truly thinks you are sick, your mind can manifest the physical ailments, even if you really are not.
So really all just mental manipulation and illusions. There are a few songs this does not really explain though.

Fiery doom, the guy just has alcohol in his breath, which he spews forth and ignites, just like a firebreather.

Elven adagio- the vibrations in the song produce a elevated healing effect causing increases in blood clotting and promoting heightened regeneration of cells. Like a cat's purring effect or something.

Vibrato = shockwave of sorts

piercing dissonance, we all know high frequencies can shatter glass

All perfectly rational non-magical things that can be done with a drunk person's voice.