Formal ;
あの、もしよろしければ、今晩、御食事を一緒にどうですか(しませんか)?
Ano, moshi yoroshikereba, konban, oshokuji wo isshoni doudesuka (shimasenka) ?
When u use ask someone out, u should say this with checking the someone's face with feeling. that would be best. :)
With friends ;
夕飯、食べ(に)行かない?
yu-han, tabe(ni) ikanai ?
飯、行こ~!!!
meshi, iko~!!! ^^/