My Oxford Dictionary of English Etymology says
imaginary animal invented by 'Lewis Carroll' (C.L. Dodgson) in 'The Hunting of the Snark', 1876.
Is that it? There's gotta be more to it than that! snark meaning "to snort" dates from 1866 according to the Online Etymology Dictionary, but I don't know the source of this. This easily predates 1875, when most of the poem was written (at least according to The Life of Lewis Carroll by Florence Becker Lennon, 1962).
Sources agree that snarky, meaning "crotchety, snappish" or "irritable or short-tempered; irascible", is derived from the verb snark "to annoy" or "to nag". The earliest citation for snarky is from Edith Nesbit in 1906.
1906 E. NESBIT Railway Children ii. 49 Don’t be snarky, Peter. It isn’t our fault.
Since words tend to show up in speech before they show up in writing, it is possible that snarky was around when Carroll wrote his poem. Or snark, for which the earliest citation is from 1882.
snark, 2. intr. and trans. To find fault (with), to nag. 1882 Jamieson’s Sc. Dict. IV. 314/2 To Snark,..to fret, grumble, or find fault with one. 1904 E. NESBIT Phœnix & Carpet x. 185 He remembered how Anthea had refrained from snarking him about tearing the carpet.
There are two possible derivations for snark. According to Merriam-Webster, snark "to annoy" is perhaps an alternation of nark "to irritate". (More about nark below). The American Heritage Dictionary says of snarky: "From dialectal snark, to nag, from snark, snork, to snore, snort, from Dutch and Low German snorken, of imitative origin."
Fernando Soto, in The Consumption of the Snark and the Decline of Nonsense: A Medico-Linguistic Reading of Carroll’s ‘Fitful Agony’ (in The Carrollian 8) mentions the word snarker "a cinder", as in "The cake's burnt to a snarker" (from The English Dialect Dictionary (vols. V), p. 572).
It's been long debated how LC came up with the word, it may be a portmanteau of shark & snail, perhaps "flavored" by a (collective) unconscious germanic memory?
There are many Germanic words containing the phonestheme sn- and having to do with the nose. Pokorny connects snorken with Proto-Indo-European *sner- "expressive root of various verbs for making noises". This is the source of German schnarren "to buzz", and also snorkel from German schnarchen "to snore", snarl from Middle Low German snarren, sneer, and perhaps Norn, from Old Norse (as in "the whisperer"). And also Norwegian-Swedish snerka "to snort", Swedish snurka "to groan", Old Norse snǫrgla "to groan", Norwegian-Swedish snarva "to growl, bare one's teeth".
There is also *snu-, a form limited to Germanic languages, and imitative of words connected with the nose. This apparently gives us snot, snout, schnoz, snuffle, sniff, snip, snap, snub, and snatch. To make things even more confusing, snore, snort and sneeze are from PIE *pneu- "to breathe" - Old English fnora and fnēosan. Compare Old Norse fnȳsa "to pant, sniff, snort", Middle High German pfnusen "to pant, sniff, snort, sneeze".
The sn- phonestheme could have influenced Carroll's choice, but unfortunately the poem is silent on the subject of the Snark's nose, and lacks any other sn- words in connection with the Snark (altho the Bandersnatch's jaws "Went savagely snapping around").
The Urban Dictionary says of snark: "Combination of "snide" and "remark". Sarcastic comment(s)." But I'd trust the Urban Dictionary as far as I'd trust a very untrustworthy thing.
Now, nark. This is the other possible source of snark "to annoy", if it's not derived from snorken. Wordorigins has a good history of nark. The Oxford Dictionary of Modern Slang (1993) says (I'm omitting the first sense because it's "mainly Austral and NZ"):
2 Brit a A police informer or decoy. 1860-.
b A policeman. 1861-.
verb 3 trans. To annoy, exasperate; often in passive 1888-.
4 trans. To stop; mainly in imperative in the phr. nark it. 1889-.
6 intr. To complain, grumble. 1916-.
[From Romany nāk nose.]
Wordorigins points out that the derivation from Romani is problematic, but that it is the most likely one. Romani nāk would be related to Hindi नाक nāk, Prakrit ṇakka, and Sanskrit नर्क narka, all meaning "nose". Probably also Sindhi نَڪُ naku , Kashmiri नाख् nākh, Panjabi ਨੱਕ nakk, Gujarati નાક nāk.
According to Watkins, these are all from Indic *nakka-, an expressive form of PIE *nas- "nose", which makes nark cognate with nose! Compare Sanskrit नस् nas, Latin nāsum, German nüschen "to dig with the snout", English nose, nuzzle, Russian нюхать njuxat' "to snuffle, sniff, smell".
Snarkskii seems to be a Slavic surname, for which the American spelling might be Snarsky.
The Snark Avenue Theatre shows late-night movies in Daniel Pinkwater's novels The Snarkout Boys and the Avacado of Death and The Snarkout Boys and the Baconburg Horror. "Snarking out" means sneaking out in the middle of the night to watch movies. Also check out Lizard Music - no snarks, but a great book.
Nothing conclusive, so no conclusion.
Then the bowsprit got mixed with the rudder sometimes:
A thing, as the Bellman remarked,
That frequently happens in tropical climes,
When a vessel is, so to speak, "snarked."
Update: more snarkian etymology.