1- You need not/do not need to shout at me! I can hear you very well.
2-I am afraid you can't take all your toys with you, girls. The car is too small. -- "should" does not work here
3- You have to/ need to/must get a visa to visit London. but I don't think it's expensive.
must: to force to a course of action in order to fulfill some need, like: We must hurry if we're to arrive on time
4- Can't you see the sign, young man ? You are not supposed to/must not/should not ('must' is stronger than 'should') drive so fast on this road! It's forbidden! In an exam, I would mark only "must not" as correct.
Do not worry, even educated natives struggle with modals. It is a minefield.
An idiom for today that has just crossed my mind:
Student or Learner