Eh, I may be wrong, but after all this time, not even my second core can do anything useful for Oblivion, let alone three others.
While Oblivion by itself does not really "not give a damn about another core" because it can use multithreading for a bit of stuff like physics calculation (or something, I forgot), the core engine like AI and all other heavy stuff won't (I did say it can use multi threads, but the processes they multithread is not really important or demanding). As such, while you can't say Oblivion doesn't take advantage of multicores, you can't say it does too.
Oh, and last thing I heard about this is Bethesda doesn't seem to give a damn about the dawn of multicore processors for Oblivion. They will think about multicores for ES V, but for Oblivion it's another update it'll never get