On my second home LAN PC, Oblivion runs on medium or so level of detail;
Intel Pentium D 945 @ 3.4ghz (2*2mb L2)
ATI Radeon 9600
4GB XMS2 RAM
I must say that I am unsure about AMD dual cores but if anything is to go by you may be able to run it on medium or so settings. Use the Oblivion Tweak Guide online to help stream the game a little better buy modding the .ini file.
Alternatively you can download from TESNexus.com the OLDBLIVION patch which lowers the overal detail package for older rigs (LAST RESORT ONLY)