garygnu, thanks for the effort in translating to a kid’s level. I think this might still be too much for 4 year old (who might just as easily not remember he asked the question this morning).
Is there any non-answer that might somehow keep his level of curiosity in these matters? I don’t want to hit him in the head with an answer that will mean nothing to him, but at the same time I want him to keep asking these questions.
Rather than try to explain it to him I’d show him as follows. Fill a sink with water and wait just a bit until it looks like it’s still. Then open the drain and have him watch. Pretty soon you will see the water spinning around the drain as it leaves.
Explain to him that originally the earth was made up of small pieces of gas and rock and liquids. Gravity attracted them towards each other just like the water went towards the drain. Even though it was very close to still when it started, there were very small currents in it just like there were still small currents in the water – so small you couldn’t see them.
As they got closer to the center (the drain), the currents went faster and faster. It’s probably easier to say at this point that energy was conserved rather than angular momentum even though that’s not really right. The “energy” of the particles rushing towards the center stayed as the “energy” of the Earth spinning just as it did with the water.
Awesome. The bath tub drain is one of those things that have always fascinated him. Thanks.
When I was finished it looked like a 7-9 year old explanation. I think the bathtub drain analogy is probably the best thing to start with.
Do you have a chair that spins? You could demonstrate conservation of angular momentum using such a chair.
He is having some trouble with the word “avocado” right now. Conservation of angular momentum should go smoothly, for sure. 
So is there still a detectable spin to the universe? (I know, i know, relative to what?) How about galactic clusters? Can we even detect spin in something so large?
In the Universe as a whole, there’s none detectable, and we have reason to believe (though we probably won’t ever be able to prove it) that there’s none at all.
But in everything short of the entire Universe, yes, everything has rotation.
Get a couple magnetic marbles and let them roll toward each other on a smooth surface. If your aim isn’t quite perfect they’ll change direction as they approach each other. When they stick together, they’ll spin.