1)Grunge down- not sure, I think it means to dress like a slob...??
2)Drab up - again, I am not 100% sure - possibly someone's investigating something painstakingly, taking a very long time to look for things.
3)What kind of party “party slumber” is? - it's a sleep over party.
4)Pop quiz- it's a quiz where questions come unannounced and without prior warning.
5)He doesn’t know which way is up (what does up mean?) - he is confused.
6)Is “get in” used for motorcycle? I would say "get on".
The word like replaces here "Do you think I remember?"
It's a very common way of talking among young people where almost every other word is like . It can be terribly annoying. Add another popular word "so" ( as in " I am like so hungry") and you have a perfect example of something we like to call a ditzy talk.