Oblivion does not like two displays when it auto-detects and configures video settings on the initial game run.
- Go to My Documents - My Games - Oblivion and delete the file named Oblivion
- Disable the display that the game is not running off (In windows, not the monitors power button)
- Run Oblivion and it shouldn’t crash (for this specific problem)
- Exit Oblivion and turn on the second display.
When you load Oblivion again, it should start fine whether you have one or multiple displays active. It seems to be an issue with the way it detects multiple screens - I’ve seen mention that they try to use _both_ screens in a weird multi-monitor see-everything mode.