Currently being in the Army, I can state that the term "Jody Call" is still in use, but "cadence" is the more common term. There are two basic types: marching (quicktime) and running (double time,) and they aren't generally interchangeable. The mentioned "I wanna be an Airborne Ranger" is a running cadence, as are most of the calls about Jody. Another common thread. "One...Two...Three and a quarter, I got a date with the General's daughter - or - wish I had some scotch and water. A different type of running cadence is used as soldiers become winded during a long run: the caller sings verses while the formation echos a sings a single phrase as separation. Example:

Woke up about a quarter to three! Hard work, work! Little girl it was you and me! Hard work, work! Woke up about a quarter to four! Hard work, work! With the First Sergeant at my door! Etc.

A good caller can adlib this type indefinitely, using common couplet strings from other cadences:

Put me in a barber's chair, spun me round I had no hair...

Nine to the front and six to the rear, that's the way we do it here...

Issued me a hand grenade, should have seen the mess I made...

Use to drive a Cadillac, now I hump it on my back...

A common marching cadence: Hey, Hey, Captain Ja-ack (soldiers echo) Meet me down by the railroad track. (echo) With that rifle in my hand (echo) I'm gonna be a shootin' man (echo)

Hey, Hey, Captain Ja-ack (echo) Meet me down by the railroad track (echo) With that bayonet in my hand (echo) I'm gonna be a stabbin' man (echo) ...a shootin' man (echo)

Etc.

As the Army becomes more politically correct, the cadences have become more tame, both sexually and with respect to violence. Most senior commanders either forbid or discourage singing cadences that refer to sex or are too gory (napalm sticks to kids). I know some pretty funny ones if anyone is interested, but won't bother unless there is a request.

Brad