Idiom - Allegory - Allusion - Anagoge

idiom is a group of words established by usage as having a meaning not deducible from those of the individual words (e.g., rain cats and dogs, see the light)
allegory - a (story, poem, or picture) that can be interpreted to reveal a hidden meaning (typically a moral or political meaning)
allusion - an indirect expression to something
anagoge - interpretation of a word, passage, or text (as of Scripture or poetry) that finds beyond the literal, allegorical, and moral senses a fourth and ultimate spiritual or mystical sense