What are the different schools/ movements in poetry in modernism?
Modernism, as a whole, was a movement that attempted to radically break from past traditions in poetry, painting, and the arts in general. There are quite a few poetic styles that came out of this movement. Imagism became a prominent Modernist movement in America with authors Ezra Pound, William Carlos Williams, and others. Practitioners of imagism tried to avoid the sentimentalism of past styles. They used clear, concise language, and objective treatment of a subject.
In Europe, Modernist movements can be traced to late 19th century French Symbolism and the French poet Stéphane Mallarmé as early inspirations. But Modernism came to be more directly associated with movements such Futurism, Dada, and Surrealism. Futurism stressed themes of speed and technology. Dada and Surrealism focused on stream of consciousness and nonlinear juxtapositions. One can see the connections between early 20th century scientific developments (automobiles, flight, Einstein, etc.) with a renewed interest in things technological. One can also see connections between themes of Surrealism with the developing understanding of the unconscious (promoted by Freud in the early 20th century) as well as the dreamlike work of visual artists such as Salvador Dali and Pablo Picasso.
T. S. Elliot was also a prominent Modernist. His most famous poem, "The Wasteland," is known for its use of intertextuality and footnotes. This is quite different than imagist poems. This shows the diversity of Modernist styles and techniques. Another subsequent movement in the 1930s was Objectivist poetry, continuing the ideas of imagism. (This is not to be confused with Ayn Rand's philosophy of Objectivism.)
It is difficult to make a generalization about all forms of Modernist poetry. But, most styles and movements were attempts to break from the past. You will see phrases like "free verse" as typical characteristics of Modernist works because this implies a freedom from any structures or traditional styles. However, "free verse" is not limited solely to Modernist writers.