Translation:He lives either in Sweden or in Finland.
Agreed. The sentence He lives in either Sweden or in Finland almost sounds as though there are two Swedens and he lives in either one of those "Swedens", or in Finland. An example to demonstrate my point might be: It is in either box or in the cupboard which again implies the object is in one of two boxes or in the cupboard. In practice this would not matter as we know there is only one Sweden hence it would be understood but is not correct and sounds rather awkward.
Both sentences Arnauti suggests sound fine though I would tend to prefer the former as it just sounds neater. (My preference only though.)
You could also drop the word "either" to make the sentence He lives in Sweden or Finland which implies the same as the other correct answers but is a little ambiguous in that it potentially could mean he lives in both countries at different times. I also assume that this would not be accepted as a correct answer in this instance because it does not include the word either which is central to the question being asked.
If you're talking about two en objects, yes, that's a correct sentence. But you can't follow up the sentence above with that question, because you're either comparing two ett nouns, or in reality referring to two clauses, and for referring to clauses we always use ett forms too. So it would have to be Vilket gillar han bäst? here.