Surrealism often uses exaggeration to make its point. Dali is a famous surrealist painter. He often used oversized and out of place objects in his paintings to prove his points.
Dadaism is another type that tested the limits of what was acceptable in extreme ways.
I think that you could argue that any post-modern art movements have exaggerated things in some way, in order to gain attention.
Expressionism is also a style where exaggeration is a key element. Picasso's Blue Period demonstrates this use, as do Kathe Kollwitz's, and Edvard Munch's works. Check out Jean Dubuffet as well. Caricaturing in political cartoons is another fine display of exaggeration.
I agree that one can find rich sources of exaggeration in in many modern art movements. I add that one can find this element in any period of human history.