

Maybe a stretch as it’s not parodying a song but parodies Star Wars kinda sorta? Seagulls! (Stop it Now)
Lonely Island has a few (Jack Sparrow) comes to mind but again not a direct parody of a specific song.
Richard Cheese does straight up covers but they are so stylistically different that it’s basically a parody. Chop Suey
Then there’s the classic comedy music duos: Garfunkel & Oates (Loophole), Flight of the Conchords (Business Time)
Bo Burnham’s whole Inside special is fantastic too.
Looks like I’m mostly listing comedy music and not necessarily parodies, but oh well.
I prefer the sounds made by the one on the right