I've gone through plot summaries of every Godzilla movie to date, and there's only one example of a scene where one Kaiju consumes, or attempts to eat, another. In Rodan (1956), the newly-hatched Rodan feeds on the Meganulon surrounding the egg. Beyond that, I haven't been able to find any cases of one monster feeding on another. This leads me to believe that, so far, there have been no other instances of one Kaiju actually eating another.
As per your examples, the Kamoeba corpse in Tokyo S.O.S. indicated CLAW marks, not bite marks. This led them to believe that the creature was killed in battle with Godzilla (or a similar monster). Orga, on the other hand, was not attempting to eat Godzilla, but rather to absorb his DNA.
Now, that said, it's important to note that Kaiju MAY have eaten other Kaiju "in the wild", where such things were not shown on-screen. The few glimpses we received of life on Monster Island showed the monsters fighting, but it's safe to assume that life in such a place would be similar to that in the time of the dinosaurs, with a defined food chain & pecking order. On the other hand, many of the monsters found on Monster Island are unique specimens rather than examples of an entire species.
If you're interested in learning more about Kaiju in the Godzilla canon, I highly recommend visiting the Godzilla Wiki site. It has detailed profiles about pretty much every Kaiju featured in the Godzilla universe, including dietary requirements & natural behavior (when such information is available for the monster type). There are also a range of comics & novels featuring Godzilla, most of which I'm not familiar with. It's entirely possibly that another example exists there.
Credit: Thanks to @WillFeldman for pointing out the Rodan reference.