Within each word, the consonants above are still in the correct order.
Below is the quotation in its correct order, but showing only the vowels and spaces:
A _ _ I _ _ _ E _ O _ _ I _ _ E _ _ E _ O _ E O _ I _ _ I _ I _ U A _ I _ _ _ _ A _ _ _ E _ O _ _ _ _ A _ _ _ O _ _
From Amazing Mind Benders Calendar 2014 by Puzzability, Workman Publishing, New York. Puzzle for September 13-14.