Do the two iPhones receive the messages? I have set my Apple ID on two iPhones already and I'm wondering if the other iPhone will receive my messages?

The phone I'm using has service but the other one doesn't.

I was thinking only the messages sent from iMessage, but I don't know so. Will they receive my messages?
The service-less iPhone will receive iMessages (and other notifications for other apps that register push notifications) while on Wi-Fi. You can remove the device from your iCloud account or unregister it from the iMessage and FaceTime services if you don't want this behavior.