"I wouldn't have thought so" suggests that you learned information that was surprising to you, that you previously didn't believe to be true or possible but now see that it is. "I don't think so" is giving your firm opinion in the moment based on your current knowledge/beliefs. "I wouldn't think so" is talking about something being true or possible; based on your current knowledge/beliefs you have doubts but are open to it being true. You are likely to find out about it later.

I wouldn’t have thought so. = hypothesising about the past. I don't think so. = a fact about the present. I wouldn't think so = hypothesising about the present or future.

In practice, nothing.