I agree with litteacher8. Imagery is generally used in all kinds, types, and genres of literature. You'll often see imagery in poetry because poetic writing often uses imagery to convey an emotion, sense of place, or an idea.
Imagist refers to a more specific movement in literature, namely poetry. The Imagist movement was started by Ezra Pound in the early 20th century. He wanted to propose a new kind of poetry that did not contain any superfluous language. The words in the poem would then be equal to the object, idea, or feeling they described. This is analogous to a mathematical operation where each side of the equation is equal. Extraneous words would be useless in this respect, so imagist poetry does rely on exact poetic description. Here is one example called "In a Station of the Metro" by Pound:
The apparation of these faced in the crowd;
Petals on a wet, black bough.
Imagism was relatively short-lived, although its influence is still seen sporadically in imagist-esque descriptions in literature. This movement was an attempt to break away from the past Romantic and Victorian styles of prose and poetry. Imagism was one of the Modernist styles of the early 20th century.
Imagists use clear, simple language to paint a picture. Imagery, on the other hand, is use of flowery and descriptive language, and often figurative language, to create an image in the reader’s mind. An imagist would keep things simple, and not use imagery other than specific sensory details.
An Allusion is a figure of speech that makes a reference to some outside source: people, events, literary works, mythology.
For example if I said, "Well, he's no man of steel..." That would be an allusion to Superman.
An allusion is different from symbolism because it draws on sources outside the text for additional meaning.
Starting with the first two terms:
Allegory describes a type of story wherein figures/objects/characters from the story represent figures/objects/characters outside the story. We can look at this as a mode of writing that uses a whole story symbolically.
Symbolism, however, is often used in smaller ways. An object might represent an idea or a color might represent a feeling symbolically.
A major difference between these two terms then can be seen in their scale. Allegory is always a "large scale" use of symbolism, while symbolism more generally can be used in small ways.