I've got to cut 300 short videos in 10 weeks. It's a 3-camera shoot- 1 x C300, 1 x 5D mkIII, 1 x 5D mkII. I wanted a way to cut out syncing and transcoding on the way in, and at a glance the Oddysey looks like it would be a good bet, especially as we haven't yet decided which NLE we're using yet!
I've heard a couple of rumours- firstly that the HDMI on the mkII isn't compatible with the Oddysey (although this may be possible with magic lantern) and also that the onboard monitors on the 5Ds would be disabled on connection with the recorder.
If anyone can shed any light on either of these, or alternatively if you think I'm barking up the wrong tree entirely, please get in touch.
The 5DII doesn't output clean HDMI natively. Like you said, it'll have to run Magic Lantern software which brings in other struggles. The problem isn't with the Odyssey it's with the 5DII. The Odyssey is a standard HDMI port so it'll take whatever you feed it on that connection.
Are you planning on getting an Odyssey for each camera? 3 cameras = 3 Odyssey's? That would allow you to standardize on settings right from the get go. But if you're going to mix formats then I'd recommend Premiere Pro as a good NLE solution since it plays any format without conversion (h.264, mxf, ProRes, DNxHD, etc.). Pluraleyes is probably the fastest way to sync everything if you don't have a way to jam sync to timecode.
And yes, when you plug in an external monitor to a Canon DSLR you lose the onboard LCD display (at least on the 5D3 and 5D2).