Have you sold an old phone or iPad recently? It's important to make sure iMessage is disabled on any old device.
I had this when I sold my iPhone 4S, where my email addresses were still associated with my old phone. Fortunately, I sold my phone to a friend, so I got him to log out of iMessage, Facetime and his Apple ID and I did the same on all my devices. I then logged back into them all on my devices and had him log into his Apple ID and enable iMessage and Facetime and that sorted it.
I've read numerous articles where people have had devices stolen and the stolen device still receives all their messages. It's a huge problem and one which it seems impossible to address at present.