theres a few different solutions, if you want to do it without attaching wires... then you have two solutions
a) power from the USB device port, this is normal usb voltage (5v)
b) power via DC port , but this needs to 7v-12v not 5v
(if you want to hardwire, you can attach a 5v supply onto the board where the board can be split in two... theres a post about this somewhere, and it seemed to work for me )
choice is up to you...
if you just need it run a patch standalone, then you can connect your usb battery pack to usb device port
if you need it to be powered, and connect via the device port, then you can could use a usb powersuppy with a voltage converter 5v to 9v. (only reason i can think for this, is if you want to enclosure the whole thing in a case, and expose teh device port for uploading patches etc.)
anyway 3.7v is not enough, and 5v is not enough thru the DC port.
(of course, this all assumes the midi controller is usb class compliant and doesn't draw more than the normal 500mA, but I assume you've already tested this with the axo connected to a computer)