Joe Offer, Jack was Woody's cousin.
The only thing I know about the tune; Cisco Houston recorded a version that I guess Woody sang on the radio as a solo, after Lefty Lou departed the show, it's called Old Lone Wolf and it's on Vanguard VRS 9089 Cisco Houston Sings the Songs of Woody Guthrie.

Drop whatever you are doing,
The old lone wolf is here to howl for you,
The lonesomer I get,
The lonesomer I yell, OWWWWWWWWWWWWW (wolf howl).

Mark Ross
https://www.youtube.com/watch?v=3WRD61HBlpQ