For the first two, they are sometimes interchangeable. There are two situations to consider: “literal” situations (in which you actually saw or heard something) and non-literal situations (in which you are discussing a situation with friends, rather than actually using your sense of sight or hearing.
Literal situations: Use “It didn’t look like it to me” to say that, based on what your eyes saw, you think the situation is different than suggested. Use “It didn’t sound like it to me” to say that, based on what your ears heard, you think the situation is different than suggested.
Non-literal situations: If you are discussing a situation with friends and trying to deduce what happened, you can use “look” and “sound” interchangeably. Example: A: “Do you think the company is going to succeed?” B: “Based on everything you told me and everything I’ve read, it doesn’t look like it/sound like it to me.”
“It didn’t come to me like that” is an unusual phrase and I’m not clear on what it means. In this context, maybe it means “The story/facts that I heard about are different from the story/facts that you are telling me now.” So, this phrase is not interchangeable with the others.