It's true, the word "eigenlijk" can be used in two pretty different ways. Intonation, word order and context are all important in distinguishing between them.
By the way: in this case, "eigenlijk" denotes a sudden transition to a new subject. Often it can also refer back to something that is currently no longer being talked about, or something (presumably) long forgotten. With this usage the word is usually unstressed, so it's never placed at the beginning of the sentence (unlike the English "by the way").
Actually, in fact: used to provide contrast with previous assumptions, usually when making statements. You can use it when you want to pretentiously tell people that they are wrong, when you change your mind about something, or various other common situations like that. The word is typically stressed in this case. For example:
- Eigenlijk heb ik niet zo'n honger - Actually I am not that hungry
- Wat heb jij eigenlijk met die boeken gedaan? - By the way, what did you do with those books?
- Eigenlijk is dat een veelvoorkomend misverstand - Actually that is a common misconception.
Edit: Asalade is a ninja
I'm trying to figure out whether "Where exactly do you live?" is an adequate translation, since adding "exactly" to the sentence can serve the same by-the-way function and "exactly" is vaguely in the neighborhood of "eigenlijk" - but obviously it's not quite the same. Thoughts?
In my opinion, "exactly" is not a good approximation of the "by the way" translation given here, or explained in depth by Simius. In fact, I would say it means almost the opposite. "By the way" makes a comment or question sound quite incidental or casual, whereas "exactly" is asking for very specific details.
If I ask someone where they live, exactly, it probably means I need directions to get there (and, if we haven't discussed this already, that I'm probably some kind of stalker!)
Maybe it's another of those U.K. v. U.S. things, but I've never heard "exactly" being used in an: "Oh, by-the-way" kind of sense, and to me, "exactly" means: "exactly". Or, in this case: "Give me street directions!"
Tone of voice is crucial to this! It really could go the stalker route, or the by-the-way route, in my dialect, which is why I'm asking as a question and not reporting as "THIS SHOULD BE AN ACCEPTED ALTERNATIVE!". But it seems like a possibility. I dunno; I really, really like parallel translations insofar as possible, and "by the way" doesn't parallel at all, and this looks like it could. So. Hence the question.
I really don't think I can add anything to what I've already said. In my "dialect" (not that I really think of UK English as a dialect), "exactly" is nothing like the intended (Dutch) meaning, of: "by the way", regardless of tone of voice. I would never use: "exactly" as an alternative to: "by the way". Of course, it doesn't follow that nobody would. Perhaps, in some parts of the English-speaking world, these are recognised as similar? Just not by me. Sorry, but you did ask, and I don't think it's a correct translation. I'll be interested to see what others think.
I feel as though that should be accepted as a possible English translation. I would report it, and if they agree, they will add it to the list of possible correct answers. Though, I believe, one of the more accurate translations of your English sentence to Dutch would be, "Waar ben je aan het wonen, eigenlijk." -or- "Wear zijn jullie aan het wonen, eigenlijk."