Firstly, your question should be 'What is the difference BETWEEN ....?'. When we are considering and comparing individual items, however many there are, we always use 'between'. Whoever wrote that Chinese textbook saying that 'between' is only used for two items has misled countless millions of people. Secondly, you are right that these words are different. A speech often expresses ideas or emotions. Speeches are often messages. Politicians give speeches, explaining their policies and persuading people to vote for them or for their ideas. At conferences, people give speeches to say welcome or farewell to delegates. At award ceremonies, winners give speeches to thank people for honouring them. Lectures belong in an academic context. Lectures give information. College professors deliver lectures in lecture rooms, and students takes notes. Presentations show the audience something. Presentations are often given in a business context, and usually involve different media - slides, graphs, maybe also audio and video media. If you do some research, you then give a presentation to your colleagues to present your findings to them. I hope that helps.

A lecture is a talk in an educational context. It is formal, and made by an expert, who is providing information to people who are less experienced than him/her. The audience are there to learn something. A speech is also formal, but not necessarily informative. It is also predominantly oral. A presentation is less formal, and often has an audio/visual component to it - with pictures and/or text.

From dictionary : speech == a form of communication in spoken language, made by a speaker before an audience for a given purpose: lecture ===an educational talk to an audience, especially one of students in a university An exposition of a given subject delivered before an audience or class, as for the purpose of instruction a speech read or delivered before an audience or class, especially for instruction presentation====a speech or talk in which a new product, idea, or piece of work is shown and explained to an audience eg His presentation speech eas very good