Welcome to Android Central! Are you saying that these 3rd party apps give you notification icons in your status bar, but never play a tone? And your Ringtones/Notifications volume is turned up?
That's my problem, exactly, although I don't always get an icon! I must add, however, that I only had the phone for a week - but I have been through 'Settings' and tried different things but nothing works ...
Huawei is notorious for very aggressive RAM management. Go to Settings>Advanced Settings>Battery Manager>Protected Apps. Make sure the apps in question are Protected (i.e., the system will allow the app to keep running with the screen off). If the app isn't protected, then the system might force the app to close in the background, which might prevent it from serving up notifications after the screen goes to sleep.