Welcome to the Forum. I'm not sure there is a way to disable messaging from your phone. I can tell you how to remove notifications of messages, but that may still be applied to your Verizon bill.
I would suggest you call Verizon and see if they are able to shut down that feature for you.
If you just want notifications to stop then go to Messaging/menu/Message Settings/Text Messages and uncheck Auto0retrieve and Notifications.
As mentioned above, you need to get you carrier to disable the feature. Keep in mind that blocking messages at the phone level doesn't prevent you from actually receiving them or for getting billed for them. The phone has to receive the message before it can block it.