These three words look rather similar, but have very different meanings.

An optical illusion tricks the eye.

An optical illusion tricks the eye.

To illude is to cheat or deceive. As a verb it is not often used, but here is an example: the confidence trickster (con artist) illuded the old man into investing his savings in the scam. As a noun it is very common. An illusion is an act or art work that cheats the eyes or logic into thinking something has happened, or just is. An illusionist (sometimes called a magician) is a stage artist who apparently pulls rabbits out of empty hats and saws women in half. I’m sure you have also seen those pavement drawings on the Internet where the artist, with his chalks, has created the illusion that there is a huge hole in the ground.

To allude is to refer to somebody who is known, or something which has happened, for example in history, to illustrate your point and perhaps to avoid saying something directly. For example:
He alluded to his poor beginnings when he said, “I was born in Manchester just after the war.”
“I’m not Bill Gates, you know.” This means I am not rich.
“He’s a real Scrooge.” He doesn’t like spending money and doesn’t care about other people.
It is, of course, necessary for the listener or reader to know the person or event being referred to, or the allusion won’t work.

To elude means to avoid or evade something. It is a word used more in literature and news than in speech. For example:
The thief managed to elude the police by hiding in a rubbish skip.
The solution to the problem continues to elude researchers.
The fox eluded capture by squeezing through a tiny hole in the fence.