Don't know if I'm doing anything wrong (I shouldn't be), but IMO Oblivion shadows are probably the worst shadows I've ever dealt with in the history of any game. It's just completely bad in nearly every way. Constantly flickering shadows, abrupt pop-in/ pop-out shadows depending on the player character's distance, absolutely atrocious shadows on grass, and constant problems with self shadows. The only shadow portion that doesn't bother me is the Tree Canopy Shadows.

Are there any mods or .ini tweaks that can address any of these issues? I have shadeMe (I'm still not completely sure what it does; I don't notice anything really different in-game), but that's about it when it comes to mods for shadows. I plan on installing the v2.1 of Oblivion Reloaded for a better shadow shader, but that's about it. Any other suggestions?

http://www.tweakguides.com/Oblivion_8.html should help you. Adjusting the shadowmap resolution to something over 2048 should give you better shadows at 1080p.

Honestly.. I envy what you're doing. Oblivion has not aged well in comparison to Skyrim and Morrowind so I've stayed away from it.

wait for the new version of OR.