Possibly pronounced as the "Whole Shilla-ley". With a very long a and accent on the middle syllable.
Please add references to better spellings.
Listen to pronunciation: http://cougar.eb.com/soundc11/s/shille01.wav [shu-lay-lee] (the whole thing)
http://www.yourdictionary.com/shillelagh (Irish club-like weapon)
Also: Shil-la-lah (town in Ireland) http://www.m-w.com/dictionary/shillelagh
I've known the word 'shillelagh' all my life, but I've never encountered the phrase 'the whole shillelagh'. 'The whole megillah', however, is a well-known Yinglish phrase: http://dictionary.reference.com/search?q=megillah