Concerning your question about style in Swift's "A Modest Proposal," the essay is actually famous for its style, and each element of style contributes to the work as a whole. I'll mention some of the highlights.
Swift's word choice or diction contributes to the irony of the work, beginning with the title. His choice of the word "Modest" creates irony when the reader discovers that the speaker's proposal is anything but modest. Instead it is ghastly and cruel.
He also uses "breed" to refer to Irish children, a term usually used when referring to livestock, and refers to the Irish in general as "savages," mocking the way in which the Irish are viewed by the English. The speaker suggests creating "shambles" or slaughterhouses, and assures the reader that "butchers" will be plentiful. These terms contibute to the irony of his proposal.
Swift uses understatement, hyperbole, sarcasm, a mock-heroic tone, imagery, humor, etc., to further his purposes, but perhaps the most important element of his style that I should mention is the indifferent, seemingly objective narrator. The speaker presents himself as dispassionate, rational, logical. His writing is loaded with facts and statistics. And he is careful to make sure his readers know that he has nothing against the Irish, and in fact is making this proposal in order to help the Irish.
Notice the following paragraph:
The number of souls in this kingdom being usually reckoned one million and a half, of these I calculate there may be about two hundred thousand couple whose wives are breeders, from which number I subtract thirty thousand couples, who are able to maintain their own children, although I apprehend there cannot be so many under the present distresses of the kingdom, but this being granted, there will remain an hundred and seventy thousand breeders. I again subtract fifty thousand for those women who miscarry, or whose children die by accident, or disease within the year....
Notice the matter-of-fact tone, the mathematical-like analysis. The speaker is unemotional and objective, understated and indifferent. This is vital to the irony developed in the essay. The speaker dispassionately speaks about a subject that is actually highly emotional and passionate.
I'm not sure what you mean by the style affecting the content. To me, the style certainly affects the tone of the essay and how effective it is.
I think the style of the essay is very breezy and informal sounding. It sounds like the author thinks what he is saying is totally normal and something that isn't at all strange. By making it sound so casual, he makes the proposal seem fairly realistic. Because of this, the essay is really quite effective. The style sort of fools you into taking it seriously, which is what I think Swift was trying to accomplish.
The style of "A Modest Proposal" greatly affects its entire contents, because satire depends upon a sense of humor (gallows or otherwise); the success of something like A Modest Proposal depends upon one’s understanding the precise distance between the narrator’s voice and the author’s—something that often got satirists in trouble. Swift here introduces a narrator who cares about the poverty, the overpopulation, the underemployment of Ireland; his “compassion” moves towards an objective, scientific means of alleviation, parodying at once the bizarre optimism of projectors and the callousness of the larger (English and even Irish) world towards the calamity at home. He uses the language of the accountant —“reckoned,” “calculate,” “subtract,” “number”— in order to introduce a scheme that “will not be liable to the least objection.” Cannibalism, of course, just happens to be one of the deepest human taboos. The charity depends on depravity, the humanity on inhumanity.
The speaker goes on for several pages in a mild, reasonable, hopeful voice about the particular delicacies of infants’ flesh, its seasonability (like game), the overall expenses involved. The suggestions—in the same mild, benevolent tone—get more and more gruesome: flaying, for example. The elderly, offered as another reasonable concern, are reasonably dealt with: “they are every day dying, and rotting, by cold, and famine, and filth, and vermin, as fast as can be reasonably expected.” The whole project is offered as something that will economically, socially, and politically advantage the troubled country of Ireland. The end of the piece reiterates the horrifying reality: how will anyone “find food and raiment for an hundred thousand useless mouths and backs”? The last lines declare the narrator’s disinterestedness: his own youngest child is nine, his wife is past child-bearing. Much as he’d like to, he can’t offer one of his own.