Similes: Andrew Jackson
Andrew Jackson’s "underjaw'd begin to stick out like the fo'castle of a steamboat" and "his teeth would uncover, and shine savage like the furnaces."
This simile illustrates the transformation of Andrew Jackson from a "little small bull pup" to a champion ("as soon as money was up on him, he was a different dog"). Twain compares Andrew Jackson to a steamboat, implying that he has an internal fire that propels him forward.
Twain worked as a steamboat pilot on the Mississippi river, so he drew on his life experience in this simile.
Similes: Dan'l Webster
"you'd see that frog whirling in the air like a doughnut—see him turn one summerset, or may be a couple, if he got a good start, and come down flat-footed and all right, like a cat."
This simile animates Dan'l Webster by adding visual and kinesthetic imagery. By comparing him to a doughnut, Twain reduced the frog's form to a turning circle that is easy to imagine. There are a couple of levels of absurdity as well: it's a stretch to compare a frog to a sweet treat, and since when do doughnuts do summersaults? The effect is silly and entertaining. The second similie, comparing the frog to a cat for landing flat-footed, is more conventional.
"flop down on the floor again as solid as a gob of mud"
This simile gives a feeling of the qualities of Dan'l Webster's body: gooey, flexible, and sticky. It also is a metonymy because both frogs and mud come from swamps. And it's a regionalism–Simon Wheeler uses this figurative language because it's in his frame of reference in the country.
"Dan'l give a heave, and hysted up his shoulders so like a Frenchman, but 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."
This sentence contains two similes followed by a metaphor. (In some versions of the story he uses the word "church" instead of anvil).
The combination of figurative language is lively because it draws from wildly different worlds: France, an anvil (which is used by a blacksmith for metal work), and an anchor, used on a ship.
The kinesthetic imagery of a frog shrugging his shoulders adds to the exaggerated comic absurdity of the passage. Frogs don't have shoulders, and they don't shrug. Dan'l Webster is thus personified. The word "so" implies that Wheeler is demonstrating the gesture.
One puzzle is the anti-regionalism of this simile: What would Simon Wheeler know about Frenchmen? It's a very conspicuous simile, which makes one wonder if Twain is making fun of smilies themselves.
Comparing the frog to a Frenchman is also a slur, as the French have been derogatively referred to as "frogs." This slur started out in language as a metonymy, linked by the French culinary habit of eating frogs. So it's a broad joke disguised as a description.
Simile: Yellow one-eyed cow
"with no tail and only jest a short stump like a bannanner"
This simile is pure silliness. Twain is making a surprising visual comparison of a cow tail to a banana for comic effect.
Metaphor: Simon Wheeler
When the narrator compares Wheeler's voice to a sweet tune, he is being verbally ironic: "he never changed his voice from the gentle-flowing key to which he tuned the initial sentence, he never betrayed the slightest suspicion of enthusiasm..." This illustrates his wry, somewhat condescending, tone. He implies that Wheeler is boring. This says something about the narrator and his intended audience: educated Easterners looking down upon a Western yokel.
Twain doubles this irony with situational irony, because Wheeler's story is obviously dynamic, well-structured, and colorful. It contains many pauses and emphasized words, and couldn't possibly be monotonous.