Are you on Wi-Fi or mobile data when you try to send the MMS message? If you're on Wi-Fi, try switching to mobile data and see if that makes a difference.
The bit I'm looking at in particular is the MMS proxy. The address is in the range 172.16.x.x to 172.31.x.x, which means that it's a private address that's not accessible from a general internet connection. It might be accessible from a standard Vodafone mobile data connection, or it might only accessible from the special Vodafone MMS APN.
The standard Android messaging app is supposed to use the MMS APN when sending picture messages, so hopefully EvolveSMS does the same thing. If not, and there's no way to say which APN to use within the app, you might need to switch back to the stock app to send MMS.
I gave Evolve a decent crack for a few weeks as it looked a helluva lot classier than the standard samsung messaging app, but I discovered I wasnt receiving any MMS or getting notified that i had a MMS to download if my data wasnt turned on.
Pain in the arse when i dont always have my data on to help battery drain when im out.
Had to switch to Hangouts which works mint but with no customization possible.
Not a solution but you're not the only one if that helps!
I've just tested this on my Note 3 & was able to send & receive MMS through EvolveSMS fine. My advanced APN settings are the same as your screenshot, so I'm thinking this will either be a vanilla Android/Nexus issue or a setting somewhere else.
Can you please confirm your MMS APN settings from device settings/mobile networks/APNs? Have you tried a fresh install of EvolveSMS?