slithy is a variant of "sleathy", meaning slovenly. Humpty Dumpty says it is a combination of 'lithe and slimy.' Lithe meaning active.
toves rhymes with "groves" (according to The Hunting of the Snark) Humpty Dumpty says toves are 'something like lizards-and something like corkscrews." They make their nest under sundials and live on cheese.
gyre means to turn or whirl around.
gimble is a variation of "gimbal". Gimbals are pivoted rings used, for instance, to keep a ships compass level as the ship rolls. Humpty Dumpty says it means to 'make holes like a gimblet."
mimsy is a nonsense word. Humpty Dumpty says it is a combination of "flimsy and miserable."
borogoves NOT "borogroves", as I am tempted to pronounce it. The first O is said like the O in worry, and there are no R's. Humpty Dumpty says this is a 'shabby-looking bird with its feathers sticking out all round-something like a live mop."
mome, our expert thinks, means they lost their way.
rath, again according to Humpty, is a sort of green pig.
outgrabe is something between bellowing and whistling, with a kind of sneeze in the middle.
frumious is a combination of "fuming and furious"
tum-tum was a common phase in Carrols time. It is the sound of a monotonously strummed stringed instrument.
uffish Carrol wrote a child friend that "uffish" suggested to him "a state of mind when the voice is gruffish, the manner roughish, and the temper huffish."
snicker-snack "snickersnee" means to fight with a knife.
galumphing a combination of "gallop" and "triumphant".
beamish a variant of "beaming"
callooh Two forms of the greek word "kalos" are pronounced "callooh" and "callay". Kalos means "beautiful" or "good".
chortled a combination of "chuckle and snort".