아주 is mostly use as Quite... EXAMPLE: Investors who bought Facebook's stock when it traded down to the teens are presumably ((quite)) happy. And 매우 use for something like "EXTREMELY" As Their doubles played ((extremely)) well and we didn't match their high intensity level.

rest of them are almost the same meaning and use, however, 너무 should be used in a negative sense as in; This coffee is too sweet. 이 커피는 너무 달아.

I'm not a native speaker, but as I understand, 아주 and 매우 both have the same meaning - "very". The only difference is that "매우" more often being used in literature and "아주" - in conversations.