Turning off push notifications has no effect iPhone 3G

I tried turning off push notifications for Facebook, but still kept receiving notices for every stupid little thing. Finally I just deleted the app.

On the latest update for the gmail app, it asked if I wanted to receive push notifications. I accidentally hit yes, and immediately began getting plagued with every incomming message. Like before, I went into Notifications and turned everything off for that app. It has no effect. I  tried deleting and reinstalling the app. I tried restarting the iPhone after I changed the settings. I still get the banner ad.

I need the gmail app so I can keep that account separate from the apple mail client on the phone, which I use only for work email.

I'd just delete the app, but it is a deal breaker for me not to have it.

Any suggestions???? Is there no way to shut notifications off? Do I need to get an Android phone?

Thanks!