allude [verb]: indirectly refer to something
Being discreet, the Principal will only allude to the incident when explaining the new policy to students. 

Note that allude is an indirect reference so does not fit in a sentence such as ‘In summary, the details I alluded to are numerous but simple’ because giving details is not indirect – mentioned or referred would be better words in this instance.

elude [verb]: to escape or get away from
The truant student continues to elude teachers and social workers.
The manager’s name eludes me but I remember his jolly laugh.

Remember the e in elude and escape to help get these words in their correct context.

An illusion is not real; so someone may have a false idea or see something that isn’t really there – they are facing an illusion.

Allusion is a reference to knowledge you assume your reader/listener understands, especially when referring to literary or art knowledge. For instance, I will make an allusion to Shakespeare’s work when I write: the young couple considered themselves to be as tragic as Romeo and Juliet. I can assume that most people know the story of Romeo and Juliet so the allusion explains a lot in few words.

To remember which is which, consider that illusion starts with I and often relates to a trick of the eye. Allusion starts with A and usually relates to Art and literature.