The "My Fair Ad-Man" spoof had a version of "With a Little Bit o' Luck":

You've never had a clean shave or a haircut
A bigger bum I hope I never see
Your taste is sad in choosing what you wear, but
With a little bit of soap,
With a little bit of soap,
You'll be looking just like him and me.
(CHORUS)
With a little bit, with a little bit,
With a little bit of soap you’ll look like we.

You've got real charcoal staining your grey flannel
I thought those shoes were for a tennis game
If you were on TV, I'd change the channel, but
With a little bit of soap,
With a little bit of soap,
You and Cary Grant will look the same.
(CHORUS)
With a little bit, with a little bit,
With a little bit of soap you'll look the same
With a little bit, with a little bit,
With a little bit of Lifebuoy soap!

A piece on "Up-to-Date Service Songs" had this take on "Anchors Aweigh":

Our taste's absurd, my boys
Our taste's absurd
With girls, our eyesight's blurred
We date pigs by the herd-herd-herd-herd
When on that briny deep
From June 'til May
Practic'ly any creep
Looks like the girl who married JFK!

The entire "Chinese Restaurant Song" went thus:

There's a bright golden glaze on the eggroll
There's a bright golden glaze on the eggroll
The hot egg foo yung really tickles the tongue
The tea's in the pot and the waiter's named Chung

Oh, what a glorious dinner
Oh, what great Moo Goo Gai Pan
We're having twenty-eight courses
Thanks to the family plan.

All the noodles are covered with soy sauce,
All the noodles are covered with soy sauce.
We're feeling no pain
'Cause our plates all contain
A big heaping portion of Sub Gum Chow Mein.

Oh, what a glorious dinner
We'll fill our bellies and then
One hour after we've eaten
We'll all be hungry again,
We'll all be hungry again.

They also did a Wine Lovers' Song to the tune of "Hello Young Lovers." Does anyone have the words to it?