Hawks will take any prey that they can kill. Anything from sparrows to geese! Obviously though, hawks are carnivores, so anything else they eat will be meat. Though, hawks do have a natural predator: Owls. Owls will attack and kill hawks at night (a benefit of being nocturnal). Owls have even made the Northern Aplomado Falcon critically endangered.
No owls are not omnivores because they eat mice,lizards,and snakes. So owl is a carnivorous bird. There are exceptions to this though, as some species such as Burrowing Owls may feed on seeds and fruits when prey is lacking, but for the most part they are carnivorous though. There are very few omnivorous owls, such as Burrowing Owls who on occasion may consume fruits and seeds. For the most part, owls are strictly carnivorous though.