참, 아주 mean like so, such, very. These adjectives are emphasized adverb and adjective. And it's meaning changed a little bit. Actual formal meaning is not used nowadays. So, you can just use like 'so' 'such' 'very'. For instance, You are so beautiful. 너는 참 예뻐. Such an old chair. 아주 오래된 의자. It is so old. 이건 참 오래된거네. It is so good. 이거 참 좋다! But be careful, sometimes it sounds weird in the context. You can say like this: 참 많이 먹었다. but it is not a formal expression in writing. In this case, 아주 많이 먹었다. In conversation, you can use 정말, 진짜 instead of 참, 아주. 수박이 정말 달다. 아이스크림이 진짜 차갑다. 굉장히 is the adverb, too. It is the same meaning to 참, 아주. But the scale is different to them. It is emphasized an adjective and an adverb. It means 'great' 'incredible' 이번 여름은 굉장히 덥네요. 경치가 굉장하네요. 굉장히 오래되어 보이는 집이네요.

To complete @sunny kim answer. 굉장히 is 굉장 + 히. 굉장 is derived from Chinese : 굉 means 'great', 'magnificient' (http://hanmun.vdegenne.com/굉/宏/0/굉장) 장 means 'strong', 'robust' (http://hanmun.vdegenne.com/장/壯/0/굉장) Therefore 굉장 means 'incredible', 'excellent', 'marvelous', etc... 히 is used to make an adverb Therefore 굉장히 means 'incredibly', 'excellently', 'marvelously', etc... 아주 is 'very (much)', 'a lot', 'really', ... 참 is more like 'quite' (a justified excess). It has the meaning of 'very much' but doesn't imply an extreme as the other words do.

Pretty much, yes tou could say those words basically means 'very' but there is still a difference to express in the level of extent.

In the mentioned order of your question, easier way to approach is good

참 normally comes as a prefix to express the genuine truth or a superior quality.

아주 is used when something has gone far beyond a general standard.

굉장히 would be closer to 'extreme' or 'incredible'.

Hope it helped to have you have a brief idea of those words might represent.