GerryAZ wrote: a 2007 Prius that seems to be burning a lot of oil. I don't think it is leaking because there are no spots where it is parked. It only has 180k miles on it and the engine sounds fine,
(bold, italics added)
I think that's basically it. Even in the linked Priuschat thread, Patrick Wong, who is a very knowledgeable Prius enthusiast, stated, "t's not realistic to expect the engine to remain in as-new condition forever. 135K miles is heavy usage and would be near end of life for many automobiles." And this one has another 45K miles more.
It is almost certainly a valve issue, either the seals (85% chance), or the actual valves themselves (5% chance) as they are supposed to be set every 90K miles, and based on the owner's actions, I'm doubting that has been done. It is reaching, but IIRC there is a throttle body valve which might be sticking and needing cleaning, but I don't know what effect its improper operation would have on oil consumption. It is also remotely possible that the engine overheated and it is a head gasket problem, but that is unlikely too. In the old days, they'd take the head off and do a valve job, which would probably give this Prius another 180K miles before something else wears out.
One of the best experts is here on the forum now, Cor Vandewater, it might be worth sending him a message. There is also Hobbit, at Technofandom http://techno-fandom.org/~hobbit/
who is also extremely knowledgeable. Another person here is Cwerdna, others who were very knowledgeable and helpful have left the forums unfortunately in the intervening years.