Complete mess with iMessages and SMS messages and different devices.....help
Use this apple self help tool to de-register your phone number from iMessage.  At that point Imessage will still work with an email address.  But you can't have it both ways, the problem you are encountering is that other phones ask the apple server if you are reachable by iMessage and if you are thats how the messages are routed.

You didn't ask, but you shouldn't need WIFI for iMessage to work correctly.  If it does not then likely you have changed carriers and kept the same number.  If that is the case, log out of iMessage on all devices, de-register the number with the above tool, and then re-log in, letting your number get registered.