What a queer bird, the frog are
When he sit he stand (almost)
When he walk he fly (almost)
When he talk he cry (almost)
He ain't got no sense, hardly
He ain't got no tail, neither, hardly
He sit on what he ain't got hardly
Then the song:
That's suitable for:
-- writing stories about little boys pretending to be frogs.
-- thinking the poem comes from Ogden Nash
-- learning it does not.
Instead, according to Wikipedia, the poem is an anonymous 19th century poem, and says not much more about the poem.
Musanim, which did that video, says the poem appeared in 1920s publications. This guy, who was born in 1924, says his grandpa used to recite the poem to him, so it must have been around in 1924 or earlier.
That is where the story ends. Other sites say it has appeared in other countries, Canada, New Zealand, and the like, but nobody knows where it started or who wrote it or what the story behind it, if there is one, might be.
It just exists.
And, finally, the Hot Actress, who I asked Sweetie to name but she didn't so we'll go with...
Elsa Pataky, who is in Fast and Furious 6 and plays
... I forgot what I was saying.