Allusion is an indirect reference to something; a hint: “Her remarks about her boss made an allusion to the fact that did not like him.” Remember, an allusion is not a direct reference but in fact an indirect reference to something that the speaker has on his mind.
Delusion is a false idea, belief, or opinion that is contrary to fact or reality, resulting from deception or a misconception: “He labored under the delusion that he was the greatest fiction writer ever.”
Delusion also refers to a mental disorder; a false belief strongly held in spite of invalidating evidence; especially, as a mental disorder: “He had a delusional side to him, and often thought how the whole world was against him”.
Elusion is to escape with the help of deception: “Thieves always work on the premise of being able to create an effective illusion and being able to escape capture. ”
Illusion is a deception; a false, although often pleasant, notion; a misconception: “A person’s illusion of youth ultimately fades with maturity.”