Just taught my twin granddaughters a song from when I was a lad. I think it came from a Mad magazine.
To the tune of Clementine.
In the cabinet, in the bathroom, o’er the sink who’s faucets shine;
stands a funny little bottle and they call it iodine.
Oh you funny, oh you funny, oh you funny iodine, you don’t taste good with a cookie but for booboos your just fine.
Here’s a cute one for teaching vowels.
B-A Bay
B-E Be
B-I Bicky bie
B-O Bo
Bicky, Bie, Bo,
B-U Boo
Bicky, Bie, Bo, Boo.
C-A Cay
C-E Cee
C-I Cicky cie
C-O Co
Cicky, Cie, Co
C-U Coo
Cicky, Cie, Co, Coo.
and so on…
I think that’s (B A bay…) called Swingin’ The Alphabet.
Mom taught me one that she called The Silly Song.
The horses run around.
Their feet are on the ground.
Why do they put the shore so near the ocean, the ocean?
Go get the Listerine, Sister’s got a date,
And we hope that Gramma’s teeth will soon fit Nelly.
While looking out a window,
a second story window,
I slipped and sprained an eyebrow on the pavement, the pavement.
We feed the baby onions, so we find him in the dark,
And a girl’s best friend is her mother
skid a mar inka dink
skid a mar inka doo
i love you
i love you in the morning and in the afternoon
i love you in the evening and underneath the moon
skid a mar inka dink
skid a mar inka doo
i love you
bo bo ski deetin doten
wah notin shhh
ishkabidilly ohten doten
wah notin shhh
Mares eat oats,
and does eat outs,
and little lambs eat ivy,
a kid’ll eat ivy, too,
wouldn’t you?
(Should be sung in such a way that you can’t tell they are real words.)
The version of AskNott’s song that I learned is a little creepier, but just as silly:
“Go Get the Ax”
Peepin’ through the knot-hole
of grandpa’s wooden leg,
Who’ll wind the clock when I’m gone?
Go get the ax
There’s a flea in Lizzie’s ear,
For a boy’s best friend is his mother.
Peepin’ through the knot-hole
of grandpa’s wooden leg,
Why do they build the shore so near the ocean?
Who cut the sleeves
Out of dear old daddy’s vest,
And dug up Fido’s bones to build the sewer?
A horsey stood around,
With his feet upon the ground,
Oh, who will wind the clock when I’m gone?
Go get the ax,
There’s a fly on Lizzie’s ear,
But a boy’s best friend is his mother.
I fell from a window,
A second-story window,
I caught my eyebrow on the window-sill.
The cellar is behind the door,
Mary’s room is behind the ax,
But a boy’s best friend is his mother.
I’m sure there are many other verses/versions out there as well.
Come to think of it, quite a few of the silly songs I know are a little creepy/gruesome if you think about the lyrics. Certainly some of them are unsuitable for children. Here’s a nice, cheerful number–the original writer is unknown, but these are the lyrics sung by the Corsairs, my favorite shanty group.
Oh, we sailed from port the other day,
Intendin’ to land at Botany Bay,
But it happened we were cast away,
Among the cannibal islands.
(chorus)
Hokey-pokey, winky-wum,
Bonny magoo, agoo, agum,
Heggery beggary biggery bum.
The king of the cannibal islands!
(oogabah oogabah oogabah oogabah oogabah oo)
The king invited us up for tea,
His name was Katori-katori-kachee,
And we were as thick as thick could be,
Among the cannibal islands
(chorus)
Said the king, “Would you be my son-in-law,
And marry the Princess Wishiwaw?”
Said I, “I would, your Majesty.” Hold your jaw
To the king of the cannibal islands!
(chorus)
Woman pie and baby sauce,
And little-boy pudding for the second course
He swallowed them all without remorse,
the king of the cannibal islands.
(chorus)
The end of my story remains to be told,
About this monarch so brave and bold,
He died of eating his clergyman cold,
The king of the cannibal islands!
(final chorus)
this is the song that never ends, yes it goes on and on my friend, some people started singing it not knowing what it was, and they’ll continue singing it forever just because, this is the song that never ends, yes it goes on and on my friend, some people started singing it not knowing what it was, and they’ll continue singing it forever just because, this is the song that never ends, yes it goes on and on my friend, some people started singing it not knowing what it was, and they’ll continue singing it forever just because, this is the song that never ends, yes it goes on and on my friend, some people started singing it not knowing what it was, and they’ll continue singing it forever just because,
That’s what I call a silly song 
A yellow bird
With a yellow bill
Landed on my windowsill.
I lured him in
With a piece of bread
And then I stomped
His little head.
Here’s another one–
I know a song that gets on everybody’s nerves.
I know a song that gets on everybody’s nerves.
I know a song that gets on everybody’s nerves
And this is how it goes
doo doo doo
I know a song that gets on everybody’s nerves . . . (ad infinitum)
One more . . .
Little bunny Foo-Foo
walking through the forest
Picked up a field mouse
And bonked him on the head.
And the good fairy said,
Little bunny Foo-Foo,
I don’t want you
To pick up the field mice
And bonk them on the head.
You get two more chances
Or I’ll turn you into a goon.
and on it goes until little bunny Foo-Foo gets turned into a goon.
Mblackwell, I believe you are thinking of “Mairsey Doats,” a popualr nonsense song c1938:
Ooooooh, mairsey doats and doesy doats and little lambsy divey;
A kiddley divey doo, wouldn’t you?
Ooooooh, mairsey doats and doesy doats and little lambsy divey;
A kiddley divey doo, wouldn’t you?
If these words sound strange to you, a little bit jumbled or jivey,
Sing ‘Mares eat oats and does eat oats and little lambs eat ivy’
Ooooooh, mairsey doats and doesy doats and little lambsy divey;
A kiddley divey doo, wouldn’t you?
Ooooooh, mairsey doats and doesy doats and little lambsy divey;
A kiddley divey doo, wouldn’t you?
My aunt had a million of these goofy songs. The one that stands out the most is:
Shoo fly pie, and apple pan-dowdy
Makes your eyes light up and your
tummy say “Howdy!”
Shoo fly pie, and apple pan-dowdy
I can’t get enough of that wonderful stuff!
Be Kind To Your Web-Footed Friends
[sung to the end bit of “Stars and Stripes Forever”]
Be kind to your web-footed friends,
For that duck might be somebody’s mo-ther.
She lives on the edge of a swamp,
Where it’s always cold and damp.
Well you may think that this is the end,
Well it is but to prove that you’re all liars,
We’re going to sing it again,
But only this time we will sing a little higher…
[repeat indefinitely]
Ging gong gooey gooey watcha
Ging gong gay
Ging gong gay
Ging gong gooey gooey watcha
Ging gong gay
Ging gong gay
A-ya …OONK!
A-ya kow-wa, OONK!
A-ya kow-wa, OONK!
A-ya HOY, toy, toy.
We learned it at camp. We loved it.
From Shari Lewis and Lambchop
This is the song that doesn’t end
yes it goes on and on my friends
some people started singing it not knowing what it was
and they’ll continue singing it forever just because…
(repeat ad nauseum)
Zev Steinhardt
Another favorite of mine is Man Piaba by Harry Belafonte (lyrics not posted because they are presumably under copyright).
Zev Steinhardt
My mom, originally from Minneapolis, ya, taught us some silly songs. This is the part of the I’m a Nut song that I can remember -
Took myself to a movie show
Sat myself in the very last row
Put my around around my waist
Got so fresh I slapped my face
I’m a nut
I’m a nut
I’m a nut I’m a nut I’m a nut
Boom-Boom, ain’t it great to be crazy?
Boom-Boom, ain’t it great to be crazy?
Giddy and foolish, the whole day through
Boom-Boom, ain’t it great to be crazy?
Boom-Boom, ain’t it great to be … cra-zee?
If you’re really interested, I’ll post the lyrics to “Found a Peanut.”
I went to the animal fair.
The birds and beasts were there.
The big baboon by the light of the moon,
Was combing his auburn hair.
The monkey, he got drunk,
And sat on the elephants trunk.
The elephant sneazed, and fell to his knees.
But what became of the monk, the monk, the monk.
Thanks, Eve, thats the one.
Do you happen to know of another older one called “We’re Crazy” or something like that?
I think one line goes “a barefoot boy with his shoes on stood sitting in the grass.”
Thanks.
Just thought of another one, “The Billboard Song.” I have an MP3 of that one, as well as “Fido is a Hot Dog Now.”