Elusion, allusion, and illusion are not quite homophones, though dashed close; here and hear are homophones (which word, by those in strong agreement, is exclaimed twice in the Palace of Westminster?). And, despite how much popular belief and practice might lead you to believe, neither are the words in this trio interchangeable.
Elusion is the successful hiding or escaping from someone or something. “Attempts to elude police” might be a telling phrase for some of our hotter-blooded readers. Elusion is most understood, however, at places like work or when in mortal danger. To elude either an elating stack paperwork or the curious sensation of a speeding FEDEX truck to the solar plexus is preferrable. To do both in the same day is elusory to the point of high rarity, as evading the one usually causes the other and vice vera.
An illusion is something deceptive in appearance or impression, and therefore wrongly perceived by the senses. Examples of an illusion might include the optical confoundment within a parlor trick, the thirst-driven shenanigans of a desert oasis, or the psychological prank when the person navigating every car, bike, or walking path is your former significant other. These events would serve only to illude your feeble mind further, for they are illusory.
An allusion is something for writers and other bags of hot air. I have never used one, as I believe there to be small choice in rotten apples. But others find them to be such stuff as dreams are made on. Allusions are indirect expressions or passing suggestions that are designed to call another source to mind without ever mentioning that other source explicitly. An allusive person, however, does not refer to things.
Allusion is oft confused with reference. If to allude to something requires oblique intimations that conjure association with other sources, then to refer to something requires direct and explicit indication. Therefore, in reference to the aforementioned allusive hot bags, I should refer you to both Shakespeare’s Taming of the Shrew and Shakespeare’s Tempest.