Since the current Oxford English Dictionary entry for this word has no examples later than 1664, you might assume it is deader than the proverbial dodo. It lives on, however, among a select group who are fascinated by archaic words. It is also the pseudonym of a British setter of fiendishly hard crossword puzzles.
Logodaedalus, in real life Donald Putnam, chose his name with care. A logodaedalus manipulates words with great cunning. It commemorates Daedalus, the legendary ancient Greek craftsman who created the labyrinth on Crete to house the Minotaur. Daidalos in classical Greek meant “the cunning one”. The prefix is from Greek logos, word.
A more recent variation is logodaedalist, which Nathanial Bailey defined in his 1727 dictionary as “an Inventer or Forger of new Words, and strange Terms” (forger is figurative — no criminal intent implied). A logodaedalist may be said to be a weaver of words into a rich and varied verbal tapestry. Daedalus the Greek artificer has also lent his name to daedal, which can refer to an inventive or skilful person but which was created by the Elizabethan poet Edmund Spenser to mean the diverse or fruitful earth.
There’s also logodaedaly, the skill of putting across a speech or a fluent employment of verbal legerdemain. Bailey said that it was “a goodly shew and flourish of Words, without much matter” — that is, without much substance or content. It might be worth resurrecting to throw at your favourite politician when he gives a loquacious but evasive answer to an awkward question.