Hmm, well after a little searching, I found where the preference is kept.
Your Home Folder -> Library -> Preferences -> ByHost -> .GlobalPreferences.UUID.plist (UUID is a unique set of numbers that identifies your computer, so I couldn't post that part of the name)
There's an option named com.apple.sound.uiaudio.enabled. Set that to false and it should shut the interface sounds off.
The plist file is saved in the binary form, so you can't edit it with a text editor. There's a few ways you can set this. If you have the developer tools, you can use the Property List Editor application to open it up. I have an application named Pref Setter that will also work (app is free). Click the link in my sig if you want to try it out.
You can also use the defaults command in the terminal. To set it, you would do this:
defaults write ~/Library/Preferences/ByHost/.GlobalPreferences.UUID com.apple.sound.uiaudio.enabled -bool false
Note that you don't add the .plist extension when you're using the defaults command.
You may need to log out and then back in before the changes take effect (for any of the above methods of changing the property).