진짜 = I use this to say like "ah, really?" "oh seriously?" and more when it's a surprise. Also it's a casual way.

그래요 = '그래요?' '네, 그래요' (Is that right? Yes, that's right) Kind of like a serious clarification. It's more "that's right"/"is that right?" than "really?" I use this when I want to be more respectful. ^^

정말 is practically the same as 진짜...it's common and should be uesd around friends. Do seriously say really really really? So you want to put heaps of emphasis, say 진짜, 정말?

I also use 정말 to say very and truly in a sentence. I don't use 진짜 in a sentence much, it's more of an expression...

저는 정말 좋아해요.

I like 정말 because it's like saying really/a lot... 아주 and 너무 also mean a lot but 아주 isn't used as much and is a bit more polite and 너무 has a negative connotation, like TOO much, overly etc, not just "a lot".