Hello Gouzai, No sooner...... than: immediately after or when "No sooner had he got home than the rain stopped." "No sooner said than done." hardly .....when: It refers to the occurrence of a second action just at the moment when a first action has taken place. It indicates an intersection marked by interference of the second action with the first at its very beginning.The first action is not complete and has just started when the second action probably cuts it or interferes with it. " We hardly started our meeting when the manager decided to postpone it for later." " He hardly arrived when his wife started to shower him with questions ." In this example the husband didn't probably sit down yet ,still at the door ( hardly arrived) and at this moment (when) his wife was ready with her questions. as soon .......as: It is used to indicate that the second alternative mentioned is not preferable to the first. "I'd just as soon go by train as drive". Here the person prefers to go by train than to drive. "as soon as" means as an expression : " at the very moment that' "She burst into tears as soon as she saw him."

- No sooner...than It is used in expressions showing that one thing happens straight after another: 'I had no sooner sat down than there was a loud knock on the door.' We can use the inversion: 'No sooner had I sat down than there was a loud knock on the door.' - Hardly...when It is used to say that something has just begun, happened, etc.: 'We had hardly sat down to supper when the phone rang.' We can use the inversion: Hardly had we sat down to supper when the phone rang.' - As soon as It is used to mean as early or quickly as (soon is an adverb that means 'early' or quickly' here): 'Please send it as soon as possible.' 'We’ll deliver the goods as soon as we can.' It can also be used as a conjunction: 'I'll come and see you as soon as I've finished work.' 'As soon as/Immediately the gates were open, the crowds rushed in.'