你好。应该是:She invited Smith and me to (have) dinner this evening.Smith and me-----是宾语成分。to dinner是地点状语to have diiner 是宾语补足语成分she是主语invited是谓语this evening是时间状语成分...
me 是没有问题的,as for the prep., "invited to dinner" is more commonly used in this context. It would be OK to use "invited to his house for dinner" but "invited for dinner" by its...