-Technically, it's not grammatically correct to say I'm good, or I'm doing good, so if you want to be 100% precise, and to the book, then you should say "I'm well" or "I'm doing well". -However, almost no one follows this rule, so you are free to say I'm good and I'm doing good as much as you like! It's a little bit less formal. -The difference by adding the "doing" part is very very small, so I wouldn't worry about it. Perhaps by adding "doing" you are indicating more specifically that at that moment, you are well; whereas when you say "I'm well", it is a bit more general. But essentially, they are equal. :)

In my opinion they all mean the exact same thing.

I'm not a native speaker, so I'm not going into the grammatical differences, but as far as I can tell in practice there's no difference. It's just that native English speakers are taught to initiate polite conversations by some variation of: A: Hello, how are you? B: I'm fine, and you? A: I'm fine too, thank you. [Possibly followed by exchanging more phrases, and only after this they actually get to the point.] It doesn't really matter what's said, you can notice that sometimes they don't even wait for the reply. Similarly, if you treat it as an actual question and try to answer it with anything that is not an affirmation of how well you are, it may throw them off. For example, in my country "how are you?" is more of an actual question than just a phrase, which sometimes leads to the cultural misunderstandings of us considering Americans etc. rude for asking questions without caring about the answer, and they consider us rude and whiny for answering that we sometimes actually aren't that fine. So, in short, they're just established phrases. Phrases do not necessarily need to follow logic or grammar.