Looks like I just answered my own question. I was using one of these OTG cables: USB OTG Cable - Female A to Micro A - 4" - CAB-11604 - SparkFun Electronics and apparently the cable was bad! Arghhh!!! Fortunately I had the foresight to order 2 of these in the past, and so replacing the cable got me going.
So can we power the Edison via J2 from a LiPo battery and use the USB OTG port as USB Host at the same time? I thought the USB port was only usable when external power was applied on J1 (7-15V), is that not the case?
Absolutely! I'm doing that right now. However, you apparently need to find a way to power your USB device, as the Edison's USB OTG port will not supply power to it via an OTG cable (unless there's some trick that I'm not aware of.) So what I'm doing is running Edison from a LiPo connected to J2, connecting a powered hub to the Edison USB OTG port with a female A to male micro A OTG cable, and my USB device to the hub.
I'd like to better understand the interplay among the various signal levels. Edison uses 1.8v, but USB 5v. So where are the level converters?