Satire is the use of hyperbole, irony, and humor to critique people, institutions, and even social norms. The purpose of satire is to alert people to crucial problems in society and to encourage specific changes.
In The Devil and Tom Walker, Washington Irving uses satire to criticize greedy moneylenders, shrewish women, hypocritical leaders, and biased historians.
Tom's wife is described as "a tall termagant, fierce of temper, loud of tongue, and strong of arm. Her voice was often heard in wordy warfare with her husband." In the 18th century, it was believed that shrewish women exhibited traits antithetical to those expected of a refined woman. When Tom shares the story of his encounter with Old Scratch, Tom's wife demands that he "comply with the black man's terms and secure what would make them wealthy for life." For her part, Tom's wife decides to take things into her own hands when her husband perversely refuses to comply with her demands.
She goes and meets with Old Scratch himself, taking with her "the silver teapot and spoons and every portable article of value." Washington Irving uses situational irony to critique the actions of an overbearing and shrewish wife; her actions reward her with the opposite of what she's hoped for. Instead of reaping great rewards from her efforts, she becomes the victim of Old Scratch and is "never heard of more."
The narrator tells us that "What was her real fate nobody knows, in consequence of so many pretending to know. It is one of those facts that have become confounded by a variety of historians." Here, Washington Irving is critiquing the problem of biased historians corrupting the truth about historical events. In the story, some say Tom's wife had "eloped with the household booty"; still others imagine that Old Scratch had decoyed her into a dismal quagmire." Meanwhile, there are those who support the theory that she had "lost her way among the tangled mazes of the swamp and sunk into some pit or slough." So, there's a variety of stories about the fate of Tom's wife, all suppositions engendered from the imaginations and biased perceptions of various parties.
In the story, Washington Irving also satirizes corrupt moneylenders and hypocritical leaders. Ministers and great men of the colony are portrayed as evil and untrustworthy men. Old Scratch pronounces judgment on these influential men, and they are burned up as firewood in the story: "Since the red men have been exterminated by you white savages, I amuse myself by presiding at the persecutions of quakers and anabaptists; I am the great patron and prompter of slave dealers, and the grand master of the Salem witches." Instead of God presiding over the judgment of these men, the author has the Devil do the honors, an irony.
Later, in the story, the author uses humor and hyperbole to highlight Tom Walker's hypocrisy. After enriching himself at the expense of his clients, Tom becomes religious because he's afraid for his chances in the afterlife: "He became, therefore, all of a sudden, a violent church goer. He prayed loudly and strenuously as if heaven were to be taken by force of lungs. Indeed, one might always tell when he had sinned most during the week, by the clamour of his Sunday devotion." Basically, Tom becomes religious, not for altruistic purposes, but so that he can cheat the Devil out of the bargain he's made with him.
As can be seen, the author uses satire as a sort of social commentary about life in New England in the 18th century.