Verbal Irony
The narrator describes Smiley's voice as possessing "a gentle-flowing key" when, in fact, he finds his voice “tedious.” He is being excessively polite in his description, showing off his manners in an exaggerated fashion. Twain is painting a picture of a fatuous, if good-natured, snob.
The narrator tells Simon Wheeler that the Rev. Leonidas Smiley is “a cherished companion” of his friend’s “boyhood,” when he suspects that the Reverend is actually a fiction. In this, Twain provides a humorous opportunity for comparison and contrast between the speaking styles of the narrator and Simon Wheeler. Like Wheeler, the narrator is fabricating characters. But he is indulging in much more florid language.
When Simon Wheeler says that Jim Smiley “...never done nothing for three months but set in his back yard and learn that frog to jump... Smiley said all a frog wanted was education, and he could do most any thing and I believe him.” This is ironic because, of course, frogs already know how to jump—they don’t need to be taught! Twain is making fun of both Western optimistic gumption, and the pretenses of formal education.
The narrator refers to “the sociable Wheeler” as he is trying to get away from him for talking too much, an example of understatement. He is also being generous in an exaggeratedly genteel manner. He doesn't want to be friends with Wheeler, so his sociability is in fact unwelcome.
Situational Irony
The narrator immediately undercuts the truth of the situation by doubting the trustworthiness of his friend and so the purpose of his mission: “In compliance with the request of a friend of mine, who wrote me from the East, I called on good-natured, garrulous old Simon Wheeler, and inquired after my friend's friend, Leonidas W. Smiley, as requested to do, and I hereunto append the result. I have a lurking suspicion that Leonidas W. Smiley is a myth; that my friend never knew such a personage..." Twain casts doubt upon the entire tale immediately. Every narrator in this story turns out to be unreliable. It's part of the pleasure of the reading experience to be fooled along with everyone else involved.
The narrator complains about how he was forced to listen to Simon Wheeler’s tall tales. We would expect, then, for this excessively polite man to spare us the stories that he himself detests. But the very next thing he does is to subject the reader to just those same tall tales—describing how Smiley “...sat me down and reeled off the monotonous narrative which follows this paragraph.” In a single sentence we get a compressed example of Twain's famous, irony-tinged humor.
When Smiley bets against the Parson’s wife getting better, this subverts the reader’s expectation of standard morality: “...before he thought, says, 'Well, I'll risk two-and-a-half that she don't, any way.'" Twain thus breaks the social conventions of deference to the clergy and to wives, and the story-telling convention of imaging the hero to be a good guy who wishes the best for everyone.
Dramatic Irony
Andrew Jackson’s trick is to get ahold of the rival dog’s legs with his teeth tenaciously. Then, ironically, he meets a dog with no hind legs: “Smiley always come out winner on that pup, till he harnessed a dog once that didn't have no hind legs." This is funny because Jim Smiley's rivals have beat him at his own game. This is not a test of strength between two dogs, but a trick met with another trick.
When Jim Smiley claims “...it's only just a frog” about Dan’l Webster to the stranger, we know that it is anything but “just a frog” to Smiley. He has spent months “educating” him. He is using understatement and affecting nonchalance to con the stranger. The added irony, of course, is that the stranger then cons him.
The reader knows why Dan’l Webster loses the jumping contest before Jim Smiley does: “...it wan's no use he couldn't budge; he was planted as solid as an anvil, and he couldn't no more stir than if he was anchored out. Smiley was a good deal surprised, and he was disgusted too, but he didn't have no idea what the matter was, of course…” The joke is on Smiley, and the reader is in on it. Simon Wheeler set us up for this delightful twist ending by building to this moment in the structure of his narrative: Smiley will bet on anything; his succession of bets on animals; foreshadowing with Andrew Jackson's defeat; the training of Dan'l Webster; Smiley's trusting absence in the swamp, giving the Stranger an opportunity to cheat.
