(This information may not be outdated. I no longer play the game so I won't be updating it.)
This is how to get rid of the notification sounds in the Android version of Simpsons Tapped Out.
NOTE: This is not for the types that don't mind risking losing their game/messing up your phone. It worked for me, but try it at your own risk. This also requires some technical knowledge, if you don't understand any of this, DON'T TRY IT!
This works in Android 4.1.2 (JellyBean (specifically CyanogenMOD 10 running on a Samsung Galaxy SII) and version 4.1.3 of the Tapped Out app. This may break in future versions *if* the .apk is updated (although most updates are done within the app, so it doesn't affect the .apk). And I suppose the developers could go out of their way to make sure this actually breaks the game, but I would think their time would be better spent putting in the option to turn the noise off.
This will require root access, there is no way to do this without it. Period.
First, find your Tapped Out .apk flie (it should be in your /data/app folder, called something like com.ea.gam.simpsons*), and copy it out to your SD card (DON'T uninstall it, just copy/paste). Grab your favorite .apk extraction/editor app (I use Total Commander), and go into your copy on the sd card. You need to delete all the files in the res/raw directory (these are the notification sounds). Once your done, install the modified .apk file. It will overwrite the copy there, but save all your settings (including your name).
I would turn off automatic updates (from the My Apps section of the Market/Play Store) so a new version doesn't sneak sounds back in. You'll know when you have to re-do this for a new version.
Oh, and don't ask me for the edited .apk. There's no way I'm distributing it. At all. Ever.