I have 90/360 multi visa in the Netherlands. I arrived to learn English in a month course, but course was postponed for a week. I told to immigration officer in the airport that I would stay for a month. Now I see that I need to stay here for one more week because of postponement of the training. Do I have to tell the immigration office about the situation? Do I have to register at the nearest police station office?
As long as your visa is still valid you are allowed to be in the Netherlands. So shouldn't get in to trouble over an extra week, just don't exceed those 90 days. Also, your answer to the airport official probably isn't even registered anywhere. They ask random these kind of questions to make an assessment of the person in front of them, not because they want to know the answer...
But if you stay once your visa expired you will likely get problems, especially when they check your papers when you are going back home.
As Avee said, the questioning by immigrations isn't generally recorded unless something suspicious is found and it gets extended into a police investigation (at which point you'd have been taken apart into an interrogation room at the very least).
When in doubt about your visa status, do visit a police station and ask. They can help you either clear things up or direct you to someone who can.
Your visa is good for 90 days ("multi" I guess means multiple entry visa?), so you're good as long as you don't stay more than 90 days in the country (or indeed the Schengen area). You've been 30 days, need to stay another 7, that's less than 90, so unless you have in the past spent more than 53 days already since the visa became active, or unless the 7 days would mean you're overstaying the last date the visa is valid, there should be no problem.