Let's start with the last two then go on to the other two. The only difference between wanna go and want to go is that the first one is informal speech, casual English or shortened, familiar speech. The next one is the more formal form. The meanings are the same but the first one would be used between close friends or students and the last one would be used by a student to a teacher or superior. would like to go is a polite way of saying that you want to go would like to + verb makes the statement polite. would go, however means that you want to go but there is some hesitastion. would + verb usually expresses a condition, problem (that prevents) or hesitation. Examples I would go with her but her parents will not allow it.(prevents) I would do it if he comes. (condition) I would do it but I worry if something bad happens. (hesitation) Hope this helps, John