Deleting Songs on Xbox 360: Not Directly Possible

The 360 has no music library manager. Tracks are just files on the HDD/USB.

Options

1. Delete entire Music folder — System Settings → Memory → Games & Apps → Music → Delete. (Nukes all.)
2. Format HDD/USB — Nuclear; wipes everything.
3. USB stick — Keep music on stick; unplug to "remove".

Better Workflow

Curate playlists on PC → Copy only what you want to USB → Plug in when needed.

Back up saves before any format/delete.