The four-thirds Olympus/Panasonic "RC" wireless system is completely incompatible with Canon's wireless eTTL. Them's just the breaks. The hotshoe communication protocols that are used to perform TTL, HSS, and wireless firing are all proprietary and brand-specific, just like lens/body electronic communication is. (Well, except in the case of micro four-thirds/four-thirds where Olympus and Panasonic gear are compatible with each other.) This is also why you can't do anything but fire the flash in sync on the hotshoe.
The only bit of electronic communication between a flash and a camera body that is part of the ISO standard for flashes is the sync (fire) signal. The ISO standard determines the physical dimensions of the foot/shoe, that the rails are ground, and the contact/pin in the center of the "square" is for sync. Which is why your 320EX fits on the GH4's hotshoe and fires in sync. But that's it. All the other contacts/pins and signals are proprietary and brand-specific. That the contacts and pins are placed identically in the Canon and micro four-thirds (and Fuji X and Pentax) flash gear doesn't mean much because the signals that go across them are not the same. You can, however, use a Canon eTTL cable between a micro 4/3 camera and micro 4/3 flash because the contacts are placed identically (you just have one additional contact on Canon gear that's not used).
If you want to remotely fire the 320EX from a micro four-thirds hotshoe, you're going to have to buy additional equipment, and you won't have most of the function you'd have using it with a Canon camera. If you want the full range of function on the GH4 you had with the 320EX and 7D, sell the 320EX, and pick up a Panasonic FL‑360L (aka the Olympus FL-600R, and which also has an LED video light like the 320EX) or any of the micro four-thirds RC-capable flashes. These flashes can be used as RC slaves to the built-in RC master in the GH4's pop-up flash, just as you used the 320EX with the 7D's pop-up flash.
Or. You could purchase radio triggers. I use the Yongnuo YN-622C triggers and YN-622C-TX dedicated transmitter with my 580EXII and YN-568EX and my Panasonic GX-7. I don't have TTL or HSS (unless I'm using my 5DMkII or 50D), but I do have remote power, zoom, and group control with this combination. Similarly, you could use Cactus V6 triggers. And if you only need manual firing sync, then any of the radio triggers out there should work (except the Yongnuo RF-603 Mk I triggers--they don't work on mft or Fuji X hotshoes, because the signal to autoswitch the on-camera unit into transmitter mode requires a signal that's Canon/Nikon specific; the MkIIs have a switch to explicitly set a unit into transmitter mode).