I'm buying Oblivion GOTY for the Xbox 360, but my xbox has a 4gb hard drive. I'm curious as to how much space a normal save file will take up at the beginning, and after completion of all three main quests.

Usually between 1-15MB for an average game.

Wow. So, assuming I have about 3.5gb of space, I will be able to play all of Oblivion, Shivering Isles, and Knights of the Nine without exceeding that 3.5gb?

Well the Shivering Isles and Knights of the Nine take up about 1GB by themselves once installed. You wont be able to install the actual game, you will have to play directly from the disk. It may be cutting it close depending on how much other stuff you play on there, but you should be fine if its just Oblivion.

Oblivion doesn't take up more than 1GB or so on my xbox and that's with several hundred hours played among many characters with all expansions.