An allusion is an indirect reference to something. An illusion is an erroneous perception or belief. Elusion is the act of escaping.
Examples
An allusion is an indirect reference. There are other words for direct references, including simply reference. These writers use allusion well:
Anyone familiar with the works of noted author John Feinstein knows that title could be an allusion to his 1980s book about a legendary college basketball coach and the Indiana program. [Boston Herald]
Perhaps this is an allusion to traditional theories in these fields that neglected differences between people for the sake of mathematical simplicity. [Wall Street Journal]
Because illusion is a relatively common word, most writers are familiar with it, and the word is rarely used wrongly. For example, these writers use illusion well:
George Bernard Shaw once said the single biggest problem in communication is the illusion that it has taken place. [Daily Herd Management]
In short, the owners felt they were trading their right to privacy for the mere illusion of greater safety. [Vancouver Sun]
And elusion relates to escape or avoidance—for example:
[I]t does sound as though Colonel Gaddafi’s elusion from his opponents may have come to an end. [Spechttps://www.spectator.co.uk/article/gaddafi-dead/tator]
Of course not having to deal with the swelling Proposition 8 debate would seem appealing to the California Supreme Court – elusion is one of their specialties. [comment on Los Angeles Times]