Well, this is a good question! There are so many words in English that have similar meanings, which I know can be confusing for learners. In the examples you give, normal and ordinary do have very similar meanings, but usual has a slightly different meaning. I think it’s useful here to talk about vocabulary collocation, which means words that are often used together. And when you’re studying English vocabulary, it’s worth spending some time just studying collocation. You can do this by looking at a good quality monolingual (English-English) dictionary, which explains collocation. You can also study collocation by reading texts (fiction or non-fiction) in English and looking carefully at the combinations of adjectives and nouns, and verbs and their objects. And it’s also possible to purchase specialist vocabulary books and collocation dictionaries.
But to get back to the words you asked about Hoa, I think normal and ordinary have [a] very similar meaning, which is probably: ‘how you expect something to be, not unusual or special’. So if we had a normal or ordinary day at work, it would mean that nothing particularly special happened. A normal or an ordinary meal in a restaurant doesn’t sound very exciting, but I suppose it’s better than having an awful one!
There is a slight nuance in meaning, however, when we talk about normal people and ordinary people. If we mention normal people, it probably means ‘people who think and behave in the same way as most other people’. But the phrase ordinary people may carry a nuance in meaning about wealth and social status, meaning ‘people who are not particularly rich’. So we might say:
These houses have been built for ordinary people to buy.
…which contains an indirect reference to wealth. I don’t think we’d say:
These houses have been built for normal people to buy.
… because this seems to be commenting on behaviour rather than income. Similarly, if we make a comment like
His new watch is very ordinary.
… it would be a slightly rude or negative comment. And the opposite of ordinary is, of course, extraordinary, and if we described a watch as extraordinary it would mean ‘very special or unusual’.
Now let’s get back to the other word you mention, usual. This is slightly different because it implies habit or regular behaviour. For example, my usual bus would be the one I always take, at the same time, every day. My usual newspaper would be the one I always buy. You can arrange to meet someone at the usual, meaning the usual bar, café or place where you meet. In this case it would be impossible to use normal or ordinary. Finally, regular customers in pubs often ask for their usual, meaning the drink they usually order!
Well thank you for your question and I hope this has helped!