At the moment, there's no central spot on your phone to control which notifications show up on your phone and how they behave across APPs.
For this end, you'll need to open up each application and tweak how and when it notifies you about new messages or other events.
Every APP has some settings (or Preferences) that are accessible by the More button.
Hit the button and a sub-menu of options will pop up, with Settings often among them.
In most Android APPs settings, you'll find a category for "Notification," "Alerts," or something akin.
- For the Email APP that I use for my company emails, it's labelled "Notification Settings".
Find yours and click it!
From the presented screen, you can usually change when and how an app notifies you of whatever it monitors. Taking the example of the Email APP that I'm using, I can:
un-check the "Inbox notifications" entirely to disallow notifications on the status bar.
Select a ringtone for my incoming email messages.
Set the phone to vibrate when a new email arrives.
With this options you can adjust your APP to react the way you intend.
Some system global settings may overwrite your definitions for specific behaviours setup on each APP. Also some power saving APPs like the one I use: Easy Battery Saver have global settings to save battery, included preventing the phone from highlighting or vibrating.
I've performed some successful tests using the Vodafone HUAWEI U8510 running Android OS, v2.3 (Gingerbread).
As far as my knowledge goes, the Android 2.2.x Froyo has pretty much the same notification behaviour.