Could this PC run Oblivion well (at least 60 FPS on Medium settings)?

AMD Athlon 64 3200+ 2.0 GHz
NVIDIA GeForce 9800GT
2GB of RAM

Medium settings? For sure it'll run it at that. Constant 60fps? Not likely for any system really....the way the game is programmed and the cell transitions causes inconsistent fps with this game. This isn't a shooter. But if only medium settings, you'll have an easy time achieving that with your system. But that processor is a bottleneck for your video card, so you may see dips when around lots of NPCs.

Yeah, I understand that.

I'm planning on getting a new PC around Christmas time (going to have a Core i5 and high-powered NVIDIA card). Just getting Oblivion to tie me over.

You don't need to have the framerate that high. As Tig mentions, it's not a first person shooter. You can get smooth enough gameplay with only 25-30 FPS, and that card will certainly be good enough for that. I'm running an 8800GT at a resolution of 1920 x 1200, and if I turn the AA off I can get that kind of framerate with all the graphic sliders cranked up. Plus some of the ini settings increased from the default max.

When i first played Oblivion i had:
AMD Athlon XP 2400 (2,0 Ghz)
Nvidia FX5200 Ultra
2GB of ram
Creative SB Audigy

I remember that the grass was the problem for the FPS so if you have a bit low FPS the grass is probably whats slowing down performance.