Did a Google search for Mad song parodies, as I grew up reading the book collections (such as "Sing Along With Mad" and "Mad About Verse." I remember one of the military anthems in full:

(Marine Corps Hymn)
From the neck-high mud of fo-ox holes
To malaria-filled bogs
We will march for ninety miles a day
And drop out and die like dogs

We will land on mine-strewn beaches
And we'll live with snakes and fleas
Then we'll all leave Parris Island for
Restful combat overseas!

and part of the Air Force hymn...
Off we go, into the barracks yonder,
Pulling an inspection again...
Roar right in, just like a clap of thunder
Scare the hell out of the men!

To the tune of "Aquarius" (from the musical "Hair")
When the sun is blotted out of sight
And both your eyes begin to burn
And you can't see the freeway
To make
That left hand turn
You know you're driving in the
Smog of Los Angeles!
Smog of Los Angeles!
Los Angeleeeees!