Figures of speech comprise two main categories. One category twists the meaning of words to wrest a new non-literal meaning from words that, when phrased together, have a very different literal meaning, as in the idiomatic figure of speech, "He died from laughter." Literally, this means a man met his demise due to laughter. Figuratively (i.e., non-literally), this means he laughed with vigor for a long time. Figures of speech that twist meaning are classified as tropes.
The other category enhances meaning by arranging and rearranging words and word order to dramatize, emphasize or more elegantly express the point at hand. For example, an analogy may be more dramatically made by using a chiasmus that inverts parallelism in a typical abba component arrangement. For example, consider the inverted parallelism of this: The day [a] but shines [b], but glows [b] the night [a]. Figures of speech that enhance through words, sounds, letters, word order and syntax are classified as word schemes, or just schemes.
It is clear from this brief explanation of figures of speech that The Wasteland, with a figure of speech as its very title, will be replete with figures of speech of both kinds, tropes and schemes. In this format, I can identify a few prominent ones, the first being the title. The Wasteland is the overarching figure of speech (trope/metaphor) that shapes this entire poetic treatise on the state of the world in Eliot's day.
The title of Part I, "The Burial of the Dead," is itself a significant figure of speech, also a metaphor, that establishes the central idea of the work. For Eliot, following World War I (1914-1918), Earth itself was ravaged, torn and dead, "Lilacs out of the dead land ...." This figure of speech signifies that death resulting from WWI encompasses the dead who died in battle and the dead who still breath though dead inside from horror and from the loss of dead Earth:
A crowd flowed over London Bridge, so many, 62
I had not thought death had undone so many.
“Son of man” is another important figure of speech, an allusion and metaphor, as this is to whom portions of Part I are addressed:
Son of man, 20
You cannot say, or guess, for you know only
A heap of broken images,
Another important figure of speech (trope/analogy and symbol) found in Part III, "The Fire Sermon," is Tiresias, the blind old man who sees "At the violet hour":
I Tiresias, though blind, throbbing between two lives,
... can see
At the violet hour, the evening hour that strives 220
This figure of speech is important because it represents Eliot's point and belief that the living dead cannot see, can no longer perceive, what is around them, what is true. This is also an allusion to the Biblical precept that those who see are blind, that is, cannot see spiritual truth.
Figures of speech of the scheme kind are also present, though seemingly less prominent and used for elegance and compression rather than for significance. An example is found in Part III: "the young man carbuncular." Here the word order is changed so that the adjective modifier "carbuncular" follows the head noun ("man") of the noun phrase. Standard word order would be "the carbuncular young man.” This sort of rearrangement of word order, with the adjective coming after the noun, is called an anastrophe.