This puzzle involves completing limericks with palidromes (words that are mirror images, and read the same backwards and forwards, like "RACECAR" or "A MAN, A PLAN, A CANAL, PANAMA!").
A few (non-spoilery) tips:
1) The palindromes are part of limericks, when the rhyming scheme AABBA (The first, second, and fifth lines rhyme, and the third and fourth lines rhyme). This means you can often figure out some missing words by guessing what completes the rhyme.
2) Since they are palindromes, whenever you do figure out a letter, you have figured out the other letter on the opposite side! Figure out a whole word, and the phrase is half-finished!