At Ft. Benning, 1968 we used a version closest to what Suz posted just above. The chorus as we did it was "Gory, gory," not "Glory, glory...." And we'd substitute the name of our least popular 'TAC' e.g., "Sergeant Brinker was the last to jump, the first to hit the ground ...." Other than that, that one's been about covered. Oh, but at the risk of being bashed as a pedant, it's got to be, "They took the Flying BOXCAR up to forty thousand feet," not the Flying Fortress, a bomber that wouldn't have anything to do with Airborne. The Flying Boxcar, should anyone care, was an old twin-boom two-engine plane, the C-119. We were about at the end of its tenure; later it was probably, "They took the C-one-thirty up to forty thousand feet."

Actually I don't remember literally marching to "Helluva Way to Die." We sang it if we were being trucked between training sites--just like in Band of Brothers, where they sing it on the road.

The song for the three-mile run was generally another one already noted but with minor changes. Our version always revolved around Bo Diddly

Bo Diddly Bo Diddly, where you been?
Round the world and back again.

BD, BD, have you heard?
I'm gonna jump from a big iron bird.

And so on, as above.

When they did let us march and not double-time, a standard was "Yellow Ribbon"

In her hair, she wore a yellow ribbon,
She wore it in the springtime and in the month of May (hey! hey!)
And if you asked her why the Hell she wore it,
She wore it for her trooper who was far, far away.

    Far away! (Far away!) Far away! (Far away!)
    She wore it for her trooper who was far far away.

Around the block, she pushed the baby carriage,
She pushed it in the springtime ...
And if you .... she pushed it,
She put it for her trooper ....

Sometimes it was done "for her trooper in the airborne infantry," even though that cost the rhyme.

Madamoiselle from Armentriers (pronounced ar-men-TREERS regardless of what the real French pronuncement might be) is WW I era, but it was brought back in WW II.

MfA, parlez vous? MfA, parlez vous?
MfA has not been kissed for twenty years!
Inky dinky parlez vous.

The second lieutenant carries a pack, parlez vous? x2
The 2nd Lt. carries a pack; we hope to Hell it breaks his back!
Inky dinky parlez vous.

They say this is a mechanized war--parlez vous? x2
They say this is a mechanized war; what in the Hell are we walking for?
Inky dinky parlez vous.

----

There was a Bismarck era German one that I hope I can find some day; all I know is one couplet & I'd be thankful for more. Bear in mind that the first line is just nonsense and "Schneidig" is evidently an obsolete usage, but it was:

    Zicke! Zacke! Jup hei die!
    Schneidig ist die Infantrie.

Free translation: "Ta-ra-ra boom de ay! The Infantry is snappy."

Finally, again at Ft. Benning, late sixties, we had two Irish Guards officers sent over to train with us in an "exchange program." They had a great one about a group of British soldiers going through all the miseries of service and horrors of war. I only heard it once, and only recall that the last line was about what they planned to do when they got out: "And we'll fornicate our ----ing lives away!"

If anyone can help with the last two, I'd appreciate it.

Chicken Charlie
42nd Training Company (Airborne)