Oh Chester
(source: "The World's Best Funny Songs", Esther J. Nelson, 1988; also in "The Worm Song and Other Tasty Tunes", Janet Wilson, 1993.)
(to the tune of "Yankee Doodle")

Oh, Chester, have you heard about Harry

Just got back from the army,

I hear he knows how to wear his clothes

Hip! Hip! Hooray for the army!

Actions: Point to each relevant body part as you sing the song, as follows:

Oh CHEST-er have YOU hEARd about HAIR-y

CHEST got BACK from the ARM-ME

I hEAR he NOSE how to wear his clothes (gesture to clothing)

HIP! HIP! Hooray for the ARM-ME!

Thanks very much to an anonymous visitor, who sent me this slightly different version of the song:

Oh Chester have you heard about Harry

Just got back from the army

He knows he needs not face defeat 

So hip hip hurray for the army!

With actions (same basic idea as above):

OH [make an o with your arms]

CHESTer have YOU hEARd about HAIRy

Just got BACK from the ARM-ME

He NOSE he KNEES not FACE deFEET

So HIP HIP hurray for the ARM-ME!