Saw this on one of my friends Facebook pages.
Reminded me that in almost every Popeye cartoon he was reciting that gibberish. Was it anything more than that? Or did it come from some song way back when? Or was it a result of his stroke?
In that, he was skat singing.
Yeah, I always thought it sounded like scatting, too.
Brain trauma from constant brawling.
The spinach-induced hemochromatosis can’t help.
One of my favorite Far Side comics:
A lot of old Irish songs used nonsense syllables and phrases, like “skithery-idle-diddle-dum.” And so did a lot of old sea chanties.
Popeye couldn’t often be heard singing such phrases.
That Far Side is great. I can’t believe I’ve never seen it before.
As kids, we used to sing:
I’m Popeye the Sailor Man
I live in a garbage can
I eat up the worms
and I spit out the germs
I’m Popeye the Sailor Man
I’m Popeye the Sailor Man
I live in the frying pan
I turn up the gas
And burn up my ass
I’m Popeye the Sailor Man!
cochrane, you were clearly more direct children than we were! 
I’m Popeye the Sailor Man
I live in a garbage can
I eat up the lizards
And spit out their gizzards
I’m Popeye the Sailor Man
I’m Popeye the sailor man.
I live in a caravan.
There’s a hole in the middle
Where Popeye can piddle.
I’m Popeye the sailor man.
To give a less humorous answer, he sang (as my late great uncle taught me)
I’m Popeye the Sailor Man! (Toot)
I’m Popeye the Sailor Man! (Toot)
I’m strong to da finish
Cuz I eats me spinach
I’m Popeye the Sailor Man! (Toot Toot)
That’s the part he always sang. To avoid breaking the rules, I’ll just link the full song (with slightly different spellings) for the rest of the verses. And here’s the sing-along version on YouTube.
I seem to remember that he would sometimes change the two lines in the middle to something that fit the particular short, but I can’t find any evidence of this in a quick search.
And, yes, the example in the OP is just him skatting. I think it was my first exposure to the concept. Some of his syllables are even “skit scat” and such.
The version from my childhood was . . .
I’m Popeye the Sailor Man
I live in a garbage can
I loves to go swimmin’
With bow legged women
I’m Popeye the Sailor Man
According to an earlier poster, he’s singing
[Skiddly eye do do re bim da bo
Reet skat doodly do ree bim da bob
Skiddly eye do do rum di bim da bee
Reet skay diddly eye doo rim da bob
Skeetin scattin skiddlyeye diddoo rop
Skiddly eye doo rum dee bo](Lyrics To The Popeye Song - Cafe Society - Straight Dope Message Board)
Our version was:
I like to go swimmin’
With bare-naked women
What kids in the old country sang:
Popeye was born in Paris
Under an earth worm
Eating spinach
Under a cow
And the cow did make
poop poop…
Yep, it does not rhyme because it did in the original Spanish:
Popeye nació en París
Debajo de una lombriz
Comiendo espinaca
Debajo de la vaca
y la vaca se hizo
… poo… poo…
Works better with the kid making the “poo” bit imitating the “toot” sound of Popeye’s pipe.
Generations of kids, ironically missing the point: you don’t mess with Popeye.
So keep good behavior /
That’s your one life saver /
With Popeye the Sailor Man.
Or there’s the Face To Face version, a personal favourite.