Forbidden Love
Although generally characterized as an example of nonsense poetry, this poem makes complete narrative sense. It tells a very direct and uncomplicated story of an owl and cat eloping. Thematically, it makes perfect sense that this marriage is an elopement since it is the story of "unnatural" love. In addition to two different species, either animal could be considered predator or prey of the other. Written during the notoriously repressive Victorian Era, this story can easily be interpreted allegorically as a story on the theme of forbidden love.
Mind Your Own Business
A cat and an owl in love makes no sense. This is why it is considered nonsense poetry. But within the peculiar reality of the world in which the story plays out, the unlikely relationship makes perfect sense. Neither the pig nor the turkey views the relationship as anything other than normal. The owl and cat are portrayed as being in perfect harmony. Each loves and respects the other. Most importantly, whether viewed as unnatural according to our world or perfectly normal according to their world, this union does nothing to upset the balance of nature. Both have entered this union of their own free will. That union harms nobody else. The poem is a thematic celebration of minding one's own business.
Marriage as Transactional
Throughout the poem, money is a key element. The third and fourth lines of the poem inform the reader that these two animals have set sail with British currency. Eventually, they pay a pig for the ring in his nose to become their wedding ring. This ring is forwarded as a necessity for the ceremony. Even the very fact that a wedding ceremony is required is significant. The poem is pursuing a theme that suggests marriage is more of a transactional ritual for being in love than a natural one.