I was able to play Oblivion on a single core Athlon 64 4000+ (2.2GHz). I think perhaps you will struggle a bit with a 1.8GHz single core. Your CPU probably has a performance speed of Pentium 4 3.4 GHz. A Core 2-based intel processor of 3.4 GHz would be doing circles around your CPU, probably, not counting the second core most of them have.
I am not sure, but I do think that Oblivion can actually make use of more than one core, even if the load isn't going to be even on all cores. If not, your PC will still be able to do background CPU tasks without it slowing down the game as much.
Also, what kind of video card do you have?
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