Yep it's entirely possible and easy to do.
1. Locate your Oblivion folder. Normally the directory is "HardDrive\ProgramFiles\Bethesda Softworks\Oblivion"
2. Inside Oblivion's folder, open the Data folder. Then locate the Music folder.
3. In the Music folder, you'll see 5 folders: Battle, Dungeon, Explore, Public and Special.
4.
Battle and Dungeon are self-explanatory.
Battle plays during combat and
Dungeon is, well, inside dungeons.
Explore is when you explore the wilderness.
Public is when you're inside a city, house or any other "safe" areas.
Special has the success, death and title song that play on the main menu.
5. You do not need to replace the music already there. Simply put your mp3s in the appropriate folder and the game automatically plays them. If you do want to replace a song in particular, you'll need to rename your desired mp3 to the name of the song you want to replace. (Make sure you backup the original file if you want to revert back to it!)
6. Listen and have fun!