I've actually thought about this a lot and I think I have a fairly good answer. It's clear that elites eat meat. As it's been said before, their muscle density is so extreme that they would need be almost soley carnivores. Also, in order to support their weight and general durability, their bones would have to be very large and solid, possibly composed of a harder mineral than calcium. They may obtain this from a supplementary source, or it may be a trait shared by their prey, likely due to high gravity conditions on their homeworld, in which case they probably also consume the bones of their food.
This leads me to another point. Their jaws are consistent with a species that does not in fact chew. Their mouths are not sealable, and they lack a tongue proper, so they can't really chew since they can't hold food in their mouths. This also rules out a liquid diet, it wouldn't be very practical.
Anyway, what I'm getting at is that the elites' quadfuricated jaw most likely is used to latch onto and help in the swallowing of large pieces of food, which are digested internally. They probably wouldn't have any difficulty quickly digesting large pieces of meat since their stomach(s?) would already have to process a very heavy and dense mineral for bone construction.
Basically elites probably eat like snakes. As for what they eat, they probably eat any small animals of sufficient diameter, in fact, due to the likelyhood of their homeworld being high gravity and therefore conducive to squat, flatter animals, and the fact that an elite's jaws would work best eating long narrow prey, I think that elites eat snakes.
Or at least snakelike animals.