"He lives in a different city."
Translation:Han bor i en annan stad.
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You'd use olika to differentiate between multiple things, since it's in plural. For instance: "de bor i olika städer" ("they live in different cities").
When using it in singular, its meaning is restricted to a comparison of behaviour or appearance. So "han är olik de andra" means "he is unlike the others."
Hence, "han bor i en olik stad" would mean roughly "he lives in a city that does not appear to be like", and has about the same grammatical weirdness to it.