hmm. i'm a native english speaker from the nyc region and i haven't heard those expressions. i've heard "i am going out to dinner" (and not "i'm going to dinner out"). it may be different in the uk or austrialia, etc

I agree with Eld. It sounds a little strange to American English speakers. If you say "outside" about eating, it sounds more like a picnic or something. I always say "I'm going out for dinner." or "Let's eat out tonight." Otherwise, I don't have any other expressions for eating somewhere that is not at home.