아주 and 매우 are smilart to the word: "very" in English. "무척" is frequently used in some province or senior people in daily life. I think each words are compatible with following words. 매우(more official), 아주, 되게(a little colloquial) - very 너무 (This word is litteraly used in pessimistic sentence) - too, so 꽤 - quite

I think both "무척" and "매우" is often found in written, and "매우" is seldom used these days compared with "아주","정말". In spoken we prefer to use "아주","정말","진짜". (There might be a slight difference among them in nuance or connotation, but in most cases they are quite interchangeable) For example, 오늘은 날씨 정말 좋다.(In fact, it's raining now in Seoul.ㅠ.ㅠ) = 오늘 날씨 진짜 좋네요.(more casual than "정말") = 오늘은 날씨가 아주 좋다.(more casual than "정말") You can pick one of them up because it's just a matter of a personal preference. As for "무척",I have never spit it out when talking with others. ^________^

보통은 셋 다 같은 의미로 사용합니다.

Tip 2) Waht's the difference among(between) A,B and C? ---- 1) A 와 B 그리고 C 는 각각(=서로) 어떻게 달라요? 2) A 와 B 그리고 C 는 각각 어떤 차이점이 있나요(있습니까)? 3) A 와 B 그리고 C(or A,B,C) 의 차이점을 잘 모르겠어요.

고맙습니다 차이가 잘 몰라요 :)