If I want to tell something important I've just found out to a friend of mine, how should I say: "I (have to/must/need to) tell you something." ?
Could anyone please explain the difference?
They all look the same to me in this case. You can use any one of those words and the sentence will still have the same meaning because they are all synonyms.
More: http://www.learnersdictionary.com/qa/must-have-to-and-need https://www.speakconfidentenglish.com/have-to-need-to-must/