As Psy did in his megahit Gangnam style and follow-up Gentleman, the direction of music video of Hangover is deliberately low-end style.
The music video is shot in Korea and it depicts how Koreans drink, get drunk, and get hangover hangover hangover hangover...
As the scenes are full of very Korean stuff, they may need some background knowledge to understand the hidden meaning.
I may be wrong, since I did not direct the music video. Yet as a Korean person, I can guide you what is so funny about it.
Here we go.
Scene 1. Psy is making a bomb shot domino.
Bomb shot is a mixture of glass of beer and a shot of Soju or whiskey, and Koreans love bomb shot as it expedite you get drunk.
Scene 2. Psy is drinking a hangover remedy. It's a kind of OTC medicine, and Korean people just love it. The scene is taken place in a convenient store, and Psy is eating a cup noodle and Snoop Dogg with a triangle shaped kimbap, a Korean style Onigiri. Unlike Americans eat pizza for hangover, Koreans gulp hot soup.
There are also some lyrics written in Korean, too.
Body shit miss
DAE CHE ODIL YES (대체 어딜 예쓰 / Where the hell, yes?)
QUIKORI MOCHA GETSU (꾀꼬리 못 찾겠어 / Can never find)
Eeny Meeny Miny Moe
Catch a lday by the toe
AN YEPUMYUN (안 예쁘면 / If she does not look pretty)
YEPU BOIL TEKAJI PARA PIRI PO
(예뻐 보일 때 까지, 빠라삐리뽀 / DRINK, until she looks pretty)
BADU SIYO (받으시오 / Let me pour you a drink.)
Hope this helps you understand the background of Hangover.