The first scene of the book, and the first chapter generally, parodies a familiar concept in English romantic novels: the character laid up with illness, stuck in a certain place with nowhere to go. Yossarian is stuck in the infirmary with his fake "liver disease," but he's staying of his own volition. (He is lying about his disease in order to stay away from continuing bombing raids, but at this point in the narrative, the reader does not know that yet.)
In this opening, Heller is referencing plot elements in many famous novels of the English Romantic era in the early 19th century: Jane Bennett stuck at Netherfield with a cold in Pride and Prejudice; Catherine Earnshaw stuck at Thrushcross Grange in Wuthering Heights. Both of these scenarios result in marriages that drive the plot of the respective novels forward. In those novels, it is a classic narrative ploy to have a character get stuck in another house for weeks. With the character cooped up somewhere they wouldn't otherwise be, they meet and often fall in love with people with whom they wouldn't otherwise spend time.
Yossarian's stay at the hospital would remind the reader of these plot elements. But the differences between Yossarian and those sickly heroines make for funny parody: Heller inverts the gender and makes Yossarian's stay clearly voluntary. And the whole thing rides on scatological humor: "They just suspected that he had been moving his bowels and not telling anyone." Heller uses these differences to make a humorous beginning to the book.
And by parodying this concept from classic novels, Heller is amplifying his critique and parody of the war effort. Yossarian is waiting out the war by faking an illness (with fecal humor involved) like a romantic heroine laid up with a cold. This makes the war seem like a romantic trifle, something that can be evaded with a bad enough stomachache.
Milo's black market dealings are bringing him great success in Chapter 24, which Heller describes using a famous allusion:
April had been the best month of all for Milo. Lilacs bloomed in April and fruit ripened on the vine. Heartbeats quickened and old appetites were renewed. In April a lovelier iris gleamed upon the burnished dove. April was spring, and in the spring Milo Minderbinder's fancy had lightly turned to thoughts of tangerines.
Heller references the first lines of T.S. Eliot's "The Waste Land" and does so in such an obvious way that it comes across as parody. This is the beginning of the original poem:
"April is the cruellest month, breeding
Lilacs out of the dead land, mixing
Memory and desire, stirring
Dull roots with spring rain.
Winter kept us warm, covering
Earth in forgetful snow, feeding
A little life with dried tubers."
Heller is, of course, subverting Eliot: April had been the best month for Milo, not the cruelest. The references to lilacs and fruit on the vine drive the point home. But Eliot was himself subverting Geoffrey Chaucer, in the first few lines of the General Prologue of The Canterbury Tales, one of the first major poetic works in the English language (here translated into modern English):
"When that April with his showers sweet,
The drought of March hath pierced to the root,
And bathed every vine in such liquor
Of which virtue engendered is the flower [...]"
So Heller's version of April agrees with Chaucer: both find it a pleasant and fair month. But Heller's description has a sarcastic ring that is not in Chaucer. The sarcasm comes both from Heller's inevitable tone built up through the book and from the cultural knowledge of this phrase having gone from Chaucer to Heller through Eliot. Heller is making a self-conscious spoof of both. Allusions are not always made with a positive feeling to the original source: here Heller is parodying Eliot, making fun of his famous lines by using the opposite of them. (Earlier in the book, "T.S. Eliot" is used as a code name, and none of the officers know who he is; Heller, a longtime English professor, lambastes Eliot at multiple points.)
There are notable similarities, however, between the versions of April in "The Waste Land" and Catch-22. In Eliot's poem, April is cruel because even though the preceding winter was destructive and barren, life still returns; Eliot sees this as a cruel forgetting of the winter's suffering. In comparison, Milo is having an excellent April, in which he steals money from the other soldiers through his immoral schemes. This is similar to Eliot's April: Milo is pulling his own benefits out of a bad situation, like "lilacs out of dead land." Within Heller's parodying tone, the allusion to Eliot still helps to describe Milo's thieving ways.
Milo's two-timing business dealings, described in Chapter 35, are the subject of another one of Heller's contradictory, ironical constructions:
Milo had been earning many distinctions for himself. He had flown fearlessly into danger and criticism by selling petroleum and ball bearings to Germany at good prices in order to make a good profit and help maintain a balance of power between the contending forces. [...] With a devotion to purpose above and beyond the line of duty, he then raised the price of food in his mess halls so high that all officers and enlisted men had to turn over all their pay to him in order to eat.
This construction is fairly standard for Heller contradictions: Milo is "praised" for these immoral acts. At this late point in the book, after so many different instances of contradictions, ironies, and paradoxes, the reader feels another layer of the absurdity of warfare in how repetitive these constructions become. But even these constructions begin to become odd and absurd as they are repeated so many times. This gives another layer to Heller's depiction of the war: not only does it not make sense, but it is boring and repetitive.
Heller, in this ironic description of Milo, parodies standard military honorifics. Milo "earns distinctions" for a "devotion to purpose above and beyond the line of duty" in stealing from his peers; he had "flown fearlessly into danger and criticism." These sort of phrases of distinction are rare in the novel (there are few admirable soldiers or officers), so when they are used here ironically, they are yet more effective. Later on the same page, the narrator uses an economic comparison rather than a military one, to make one last ironic picture of the two-timing salesman: "Milo had been caught red-handed in the act of plundering his countrymen, and, as a result, his stock had never been higher."