If my understanding is correct, it seems like the three of them is about a groupment of people.
Kaigi (会議) is work related, while Kaigou (会合) and Shuugoo (集合) is used in the context of family & friends?
1 Answer
会議 means there is discussion (usually to decide something). It's usually used for work, but it can also be used for non-work occasions (like 家族会議).
Kaigou (会合) is less commonly used and it's a bit grander than 会議. Like 会議 it implies there is a discussion, but compared 会議 the purpose can be a bit more general (e.g. just to network, rather than discuss something specific). It also evokes the impression of fewer participants, and a shorter timespan (so more like a short but important meeting by few important people). Example is e.g. meeting between two prime ministers.
Shuugoo (集合) refers to the physical act of getting together and doesn't imply there is a discussion. For example if I say 八時に集合しよう it doesn't mean we discuss - it just means we meet up at eight o'clock.
