Choosing between OM-D E-M5, GH2, and NEX 7/6 for documentary/photojournalism photo AND video

Cy Cheze gave some good advice. i'm also going to add my two cents that is completely outside of the scope of what you are considering, so you may just end up completely ignoring me. but if you are willing to spend a bit more money, around 3k, then you could get a sony nx70 camcorder (which takes photos too, albeit mediocre ones), and that is IP54 certified against rain and dust, has 96GB of internal storage (and the camera can transfer files to a USB HD directly without a computer), a battery that lasts over 5 hours, 26mm f1.8 on the wide end with 10x zoom, optical steadyshot, 1080p60 avchd 2, infrared night-shot for shooting in total darkness, and is quite discrete with the handle for xlr inputs taken off (which is not weather sealed anyway).