I have tried a restart, switched to safe mode, switched to global and restarted in safe mode. My MMS messages are simply a group message send/reply - not even pictures...the only way to read them is via Mobile data - which I try to keep low wince Verizon took away my unlimited data plan. I can't retrieve them via WiFi - just have to eat up my Data Usage and I will be asking for a credit - I refuse to pay data overages because Verizon has a glitch.
Your phone is operating as designed. Multimedia messages (those with pictures, special symbols/emoticons, group texts) send/receive via a cellular data connection, not wi-fi. However, they count against your text package, not your data plan.