Usually apps that serve notifications provide their own ways of controlling them. You will need to open each app that you want to stop notifications from, open their settings, and look for notifications. There you will have many options including changing the ringtone, frequency, and even turning them off completely.
For example in Gmail app:
- Tap on the top-left "three lines" icon, then scroll down and tap "Settings".
- For each account you've added you'll need to tap it, and then modify the Notification settings.
- To disable notifications altogether - uncheck the "Notifications" option.
The Outlook app should have similar controls for notifications.
For apps that don't provide any way to control notifications, you can completely suppress them via Android's 4.x built-in feature. On the home screen go to Settings -> Apps -> All apps, then find & tap the app you wish to silence, and uncheck the "Show notifications" option.
On Android 5.0 and above the per-app notification overrides got more options rather than just a simple on/off toggle. See this site for details. You can long-press on the offending notification and tap the "info" icon to get several options that include privacy features, along with the above mentioned toggle.