There are so many words in English that have similar meanings, which sometimes, you would be amazed to 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. It is useful here to talk about vocabulary collocation, which means words that are often used together.

Normal and ordinary and usual 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 or a usual day at work, it would, mean that nothing particularly special happened. A normal or an ordinary meal in a restaurant does not sound very exciting, but it is definitely 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 implies an indirect reference to wealth. We do not say: These houses have been built for normal people to buy because this seems to be commenting on behavior rather than income. But we can’t use usual in this context. 

Similarly, if we make a comment like this one that
His new watch is very ordinary. Then all eyes would be raised on you as it would be a slightly rude or negative comment. And the opposite of ordinary is, of course, extraordinary, and if we describe a watch as extraordinary it would mean very special or unusual watch and everybody would be praising your description.

There is another word in the lot which is mentioned quite often, the other word is, usual. This is slightly different because it implies habit or regular behavior. For example, my usual bus would be the one I always take, at the same time, every day. My usual news paper would be the one I always buy. You can arrange to meet someone at the usual, meaning the usual bar, cafe 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.

These three simple words may sound very normal, usual or ordinary but the right use only makes sense. English is often termed as the funny language as pronunciation od same sound words sometimes go in different directions. Being English the international language of the world today is the language to be learned and followed and no matter how confusing it might go, to get successful it is important to make English your cup of tea.