You can go to Settings >> Notifications and see a list of all apps that can send you notifications. They will either be off, or send a combinations of sounds, badges, or alerts.
That would be the best place to start looking.
Or if you just want to shut them all off no matter what, there is a switch at the top to do that.
Mail and Calendar alerts are under Settings >> General >> Sounds, though it doesn't sound like that is where your sounds are coming from.