I wouldn't usually just link to a random youtube-video for no reason, but this is seriously one of my all time favourites in the genre of hilarious musical live performances.

Flight of the Conchords are a musical duo from New Zealand, they also have a tv-series featuring their music. It's the most awesome thing ever. I haven't seen the show, but all the music is on youtube.

The below video is my favourite song, Jenny, performed live. I can't stop laughing at this, it's such an awkward moment. If you would like to see more, some other of their songs are If You're Into It,
Bret You've Got It Going On and Albi the Racist Dragon.