Converting assets

Is it possible (legally and technically) to use, for example, CryEngine Assets in Unity?

Legally, you have to consider the respective terms of usage of those Cry-Assets. Typically you can read about legal restrictions in their terms of service.

Technically it’s only possible to use assets in a format that Unity supports, typically FBX or OBJ for models. If you are referring to a proprietary format, you will most likely need a converter to first convert any engine specific engines to a common format like FBX. Typically this would be done on the CryEngine side, not in Unity.