Phone won't shut up even in Vibrate/Silent mode If I set my phone to Vibrate or Silent modes, it's still making audible notifications for GMail, Hangouts, Waze, and maybe other things.

It has worked as expected for years, and then started doing this in the last few weeks.  I don't see any other setting anywhere that adjusts this.

All 3 of the main volume controls are at zero.  Is there somewhere else I should look?

The loudness of the notifications matches the loudness of the notification slider when it's not muted.  Like if I set it to high level and then go to silent mode, the notifications are still high level.  If I set it to the lowest level and then go to silent mode, the notifications are at the lowest level.

CM11, Android 4.4.4, Samsung Galaxy S Relay
It is a fact that there are elements of the audio on devices that escape the Vibrate/Silent mode you are dealing with. I was disturbed at the difficulties of closing all audio channels, too. Years ago I found an app that made all the manipulation of the sounds on my devices clear and simple: Volume Ace. It makes it clear which systems still allow audio when in Vibrate mode, or when directed to be Silent. It allows you to control the outliers right from within a single screen, rather than through multiple menus or other activities. It allows for audio profiles for time of day, etc. It allows your settings to be saved, and recalled in case of unintentional disruption. I haven't needed to play with most aspects of audio in some time.

DISCLAIMER: I am not the developer, just a long-time satisfied user. I hope you find it as useful.