I am new to PC gaming, and am replaying Morrowind with mods for the first time (loving it so far, even though I am only using the MGSO 3.0. More mods to come).

I also want to replay PC Oblivion with mods. How well would this system run Oblivion with the best graphics mods out there? It is a core i5 2320 @ 3GHz, 8 gigs of RAM, GTX 650.

It should run it fairly well, though do realize that Oblivion was not designed to take advantage of multi-core processors, so it waill be a beast when you load up many graphic mods (HD texture replacements, visible when distant (VWD) mods) that use up VRAM. Also, mods that add NPCs (and associated scripts) usually bog down the processor, so FPS rates drop. That said, your machine seems better than most. In summary, the more mods you add, the harder it gets. Crashes occur due to many things, and using up your memory or processing power is one of them. Most crashes occur due to other reasons (incorrect install, clashing among mods etc.).

Make sure you read up the blog listed in my signature for installing it correctly (do not install under Program Files etc.) and other tips and tricks.