My OED was close at hand, so I checked it out. Not a lot of help, actually. Podger is defined as "a stiff blow" (citation from 1816). Podge has two entries.
1) "anything podgy; spec. a short, fat man or woman, a short, stout, thick-set animal." Citation, 1833 (of an epaulette) "That man with the podge on his shoulder..." (of a first lieutenant)
2) "to walk slowly and heavily."
Podgy is defined as "anything short, thick, and fat; squat."
So I suppose we are left with the understanding that this is a stout, thick, heavy wrench.