That Thor’s hammer, Moljanir, first started as a metal meat tenderizer energized for an hour in a microwave. Its how it got its lightning powers…
What…?
When any adoring aunt, uncle or granma comes round to take a family photo, teach her to pose and flash gang signs at the camera!
Teach her Mousetrap:
You present your fist to somebody and invite them to “smell the cheese”. When they oblige, you flick them in the nose and yell, “Mousetrap!”
Knock knock.
Who’s there?
Banana.
Banana who?
Banana banana. Knock knock.
Who’s there?
Banana…
And so on, until you get to the “Orange you glad I didn’t say Banana?” punchline. A toddler once kept this joke up for about thirty miles when I was on a bus to Wales.
“Guess what?”
“What?”
“Chicken butt!” (laugh)
Hours and hours of fun.
I knew which book you meant before even checking the link. 
My husband babysat his older sister’s young girls, and taught the 3-yo to move her eyes independently. His sister was pissed at him, especially since her daughter discovered how funny it was to freak Mom out by rolling one eye or rolling them up into her head.
It might be funny to teach her to sing Old Plank Road. The chorus features the line, “Won’t get drunk no more”.
Or even the English version as heard in this trailer: http://www.youtube.com/watch?v=rUtX8pFl6Wc&list=UUrstvVjN1FYwuSm8IPSuyow&index=2&feature=plcp
(I’m late to the thread, but I thought you might like the link, assuming it’s not what inspired your post in the first place.)
Mr. Shoe once heard a little wee tyke - 2.5, maybe 3 - who had learned to say that sitcom-y singsong “awwww-kward” at opportune moments. He doesn’t normally like kids all that much, but I think he wanted to bring that boy home. 
“Guess Why?”
“Why?”
“Chicken Thigh!”
“Guess how!”
“How?”
“Chicken Kung Pao.”
The Nazis are coming, hooray, hooray,
The Nazis are coming, hooray, hooray…
Guess who? Chicken YOU!
Ladies Bridge Club? Is that still a thing? Do modern ladies have time to go around playing bridge? I work for a living, I don’t have time for that. 
ETA: Teach her some Yo Mamma jokes. “Yo Mamma so dumb, she thinks food stamps are for mailing food!”
Interrupting Cow?
Here’s a cooking project for her next visit. Send her home with a sample in a Ziploc baggie.
The Mahna Mahna song.
Hi, I’m new - first post. 
My (at the time) four year old nephew and I were in the back of his dad’s car on the way to somewhere, and I was trying to keep him entertained. Somehow we hit on the idea of a secret club called “The Troublemakers”. This was an instant hit, and by the end of the journey we had a secret handshake, and a motto (“Troublemakers! Troublemakers!” repeated ad infinitum).
The next time I saw them, about half a year later, I was greeted with a hearty “Troublemakers!” and a demand to do the handshake. Later, I expressed amazement that the nephew had remembered the secret club, to which my brother replied:
“We’ve… had… six… MONTHS… of… this…”
It’s great being an uncle.
Now I want to know what Diosa actually did…
I taught my friends’ daughter to say “You better check yourself before you wreck yourself!” to any visitors in their home. They weren’t very happy, but she loved saying it, over and over.
Teach her how to load and fire a pistol as a means or resolving arguments.
My dad taught all the grandkids Monty Python quotes. Especially the French Guard taunts. My nephew was saying “I fart in all directions” for months. (yeah, he got it a little wrong…)