As Matilda explains, the poem is in fact a limerick, a particular kind of funny poem which always has five lines and the same rhythm. The style was popularized by 19th century nonsense poet Edward Lear, who also wrote "The Owl and the Pussy Cat".
CS Lewis wrote the Chronicles of Narnia in which The Lion, the Witch, and the Wardrobe is the second book. The book opens with the four children being evacuated from London during World War II. When they discover a secret doorway to Narnia through the back of a wardrobe in a strange old country house, they find themselves in a land of continuous winter. Soon they become embroiled in a war between the fantastical creatures of Narnia. With so much war and metaphorical darkness it is easy to see why Matilda feels there are no 'funny bits' in the books.
Mr Pickwick is a character from Charles Dickens' first published novel entitled The Posthumous Papers of the Pickwick Club or better known as The Pickwick Papers. Mr Pickwick is the novel's main character and president of the Pickwick Club. He makes the suggestion to three other characters to journey to remote places and to report on all that occurs. The characters are all very comic and have equally exaggerated responses to different situations.