'vas-y' is *not* 'let's go'.
'va' is the 2nd person imperative form of the verb 'aller'. In english it's like 'go!'. but in French no one says just 'va', to say 'go!' we say 'vas-y'.
for example:
- je veux aller en Australie. (I want to go to Australia)
-vas-y! (go!)
well, that example was kind of weird but you get the idea.
"Let's go" is "allons-y"...when saying "vas-y" you're just telling someone to do something, the speaker is not included in that action. "Let's go play" is "allons jouer", "go play" = "va jouer".
"vas-y" can also be used colloquially to encourage someone to do something. (I guess that's what Marie Hélène and Loic were refering to.)
e.g.: -tu crois que je devrais lui demander de sortir avec moi? (do you think I should ask her out?)
-mais oui, vas-y! / allez! (= yeah, do it! / go for it!)
I hope that made sense.
"pas de quoi" is the shortened form of "il n'y a pas de quoi", which is similar to "de rien" (you're welcome)...you can use it when you do someone a favor and they thank you, well instead of saying "de rien" you can also say "il n'y pas de quoi" (literally: there's no reason [for thanking me])...but "de rien" is ok too.
e.g.: - merci d'avoir arrosé les plantes en mon absence. (thanks for watering the plants when I was away)
- de rien / il n'y a pas de quoi. (you're welcome)