An allusion is a reference to a well-know story, event, piece of literature, Bible story, or even movie, that makes a complex point with only a brief reference. For example, if I say, "He thinks he is Zeus," you know that I think the person we are talking about has a power obsession. Another example is if I say, "She was his Delilah," you know that a man was betrayed by the woman he loved and trusted.
An idiom is a type of figure of speech that means something other than what it actually says. An idiom cannot be understood literally. It must be understood figuratively. For example, if I say, "She has a bee in her bonnet," you don't worry that she will get stung. You know, instead, that she has an idea in her mind that she will not let go of; maybe she is continually insisting that I go on a blind date with her second cousin twice removed.
I've never heard of asking for allusions (references to a well known thing like mythology, the Bible, Shakespearean plays, classic movies) that comprise idioms, but I'll give it a shot, which is an idiom meaning give it a try and a basketball sports allusion.
An example of an allusion with an idiom might be: "He turned out to be selling a horse of a different color." The allusion could be to the classic movie The Wizard of Oz, which virtually everyone knows, or Shakespeare's Twelfth Night. The meaning of the idiom ("horse of a different color") is that the topic at hand is different from what was expected as the topic. In this example, the idiom might mean she was expecting the topic of marriage and he was only offering the key to his apartment.
Another allusion with idiom might be: "The news was a bolt from the blue." The allusion is to Zeus again (he really gets around) who is famous for hurtling bolts of lightning. The idiom "bolt from the blue" means something has happened suddenly and unexpectedly. In this example, the idiom means that someone received sudden and unexpected news, which could be good or bad news.
Good sources for idioms are UsingEnglish.com's English Idioms & Idiomatic Expressions, with an alphabetical listing of thousands of idioms, and Phrases.org.uk's The Phrase Finder, which gives the origins as well as meanings of many English idioms. The University of Southern Carolina at Pembroke has a very thorough Glossary of Literary Terms, including allusion, and Carson-Newman College's Literary Terms and Definitions: I has a very good definition of idioms.