When I first came across this word (as Howling Fantods) in Inifinite Jest, I found it unlisted in the dictionary and assumed it was another word invented by David Foster Wallace. Later I found prior usage in Thomas Pynchon's 1973 book Gravity's Rainbow:
... it was always easy, in open and lonely places, to be visited by Panic wilderness fear, but these are the urban fantods here, that come to get you when you are lost or isolated inside the way time is passing...
Searching the internet found a history of this word's usage on the site The word detective.
The "fantods" (no one ever seems afflicted by a single fantod) are, as the American Heritage Dictionary puts it, "A state of nervous irritability...a fit." The venerable Dictionary of American English quotes an 1899 definition which rounds out the picture: "Fidgets, restlessness; a state of anxiety or excitement," and dates the word's first appearance to 1839. Some sources call the fantods a "mythical disorder" or equate them with a simple stomach ache, but probably the best synonym would be "the willies," or what our over-therapized society now blandly calls an "anxiety attack." Other synonyms include the screaming meemies and the heebie jeebies (thanks ideath).
Looking for the origins of "the fantods" is enough to give you a case of them. The American Heritage Dictionary prudently says "origin unknown," the dictionary equivalent of "no comment." The Oxford English Dictionary comes to the rescue as usual, pointing to the colloquial form "fantad," probably based on "fantasy" or "fantastic." A related word of similar origin, "fantigue," was popular in the 18th century and used by Charles Dickens in The Pickwick Papers. Mark Twain was evidently fond of "the fantods," and you'll find the word in Huckleberry Finn.