While I haven't tried it frequently, when I did a check a few months ago on EF it seemed that EF showing O did not reflect reality in terms of partner availability.

What is quite certain is that DL has multiple classes/levels of inventory when using Skymiles on it's own flights and just because there is inventory in any particular one of those levels for Skymiles does not translate into any inventory for partner bookings on DL flights. Award bookings in lower award levels also often depend on more than just inventory in a particular class as they generally also require roundtrip bookings (particularly on international awards) and meeting advance purchase requirements (so you can't always definitively tell what actual class inventory is available on a DL flight when doing a Skymiles award search).