When I installed Oblivion, a clean install, the directory tree is like:

Oblivion\Data
Oblivion\Data\Music\{Battle,Dungeon,Explore,Public,Special}
Oblivion\Data\Shaders
Oblivion\Data\Textures\Effects\TerrainNoise.dds
Oblivion\Data\Video

After following some nice reading at http://sites.google.com/site/oblivionpoinfo/walkthroughs/baininstallguide/organize, check out the bottom of the page. He keeps backups of original files but I don't have Meshes folder...

Just wondering if something went berserk with my install or if it's just an extra backup that he made.

Nothing to worry about. Vanilla Oblivion keeps all Meshes, Textures (with one exception) and all Sound in BSA files, so there is no Meshes folder. You may want to back up the BSAs, though.

All the original files are in the BSA files.

The ones that you see loose in those folders are installed by the 1.2.0416 patch. They're really the only ones you need to back up, since the BSAs are never altered by any mods.

Of course, you should back up the BSAs if you plan on editing them as well.