Since i prefer "insane" graphics i could drop few dimes.
Oblivion is single core game so something like 3,2ghz+ cores for cpu.
having good graphics card helps with frames. I got 6gb card and frames are generally very high with ENB on. I'd say having 4gb is at least mandatory if you use higher than vanilla textures etc.
You can get oblivion to modded skyrim level but places like say TES diesel and Snus Dungeons overhaul can make the engine cry even without enb. They are so cluttered and i guess Oblivion is having trouble when theres like more than 8 npcs in the view + 370 rocks and plants in your grid . Based on memory usage with CS. CHrocks are badly done meshes.
short: You can do skyrim visuals with 4gb+ card, you need over 3ghz cpu core, It can be stable but you need to be a bit choosy with stuff. (dont use many script mods together, gamebryo is shit ass engine)