I've never had anything from Omaha Steaks, nor have I ever seen their packaging up close.
Bearing that in mind, I can only give some general comments as follows:
Most meat vacuum packing is fine to cook in but only of there is no absorbent pack in there with it, or paperboard (like in some commercial bacon packages). It should be just the vacuum pack plastic. The semi-flexible cut resistant plastic sheets or strips that are sometimes placed in the bags as bone guards, I believe are food grade nylon, and should be fine to leave in.
The vacuum sealed trays might or might not work depending on what plastic the tray is made out of. I would not attempt to sous vide vacuum sealed styrofoam either. You should always remove any labels or stickers from the outside of the package, as these will come off in the hot water and likely end up in the impeller.
Just looked at some google images of the Omaha Steaks packaging, can't find any photos of the bottom (flat) side, but looks like a heavy duty cryopack of some sort, which I think would be fine.