The lilting rhythm of "Jabberwocky" helps the narrator's cause. It makes the poem easy to remember (so that he can tell it to you around that campfire), and it keeps the story moving forward at a regular clip. (Think: "and THEN and THEN and THEN and THEN!")
All the exclamation points in the middle are what give our storyteller his cues to gesticulate wildly at us while relaying the epic battle, and so even though the rhythm stays constant, we have some good changes in volume.
Speaking of volume, there's also all this wonderful onomatopoeia – that is, words that sound like their definition (think "hiss" and "buzz"). Phrases like "snicker-snack!" (18) and "whiffling" (15) and "galumphing" (20) and "chortled" (25) (the last two of which are officially recognized English words now) give us sound cues that help us not only see, but hear the events going on in the poem. After all, it's a nonsense poem – the words were mostly chosen or made up for their sound, not their sense.
Wow – after all this, "Jabberwocky" might be the ultimate "Sound Check" poem.