Our apartment has oiled oak floors, even in the kitchen. They don't seem to have any sort of sealant and anything spilled just gets absorbed really easily. How do we clean them?

Unfortunately, you can't. If the stain is in wood, your options tend to be: sand down to the point that stain soaked in (which may not be possible), sand and seal, or sand and paint.

Best option is to prevent the stains from happening, which isn't easy, I know.

We have those floors too. I use something called Pflege Wachs (Saicos Coating Systems). It seems to get the stains out pretty well. There's another product by this company- I think it's some kind of Seife for daily use (can't remember the exact name as I ran out of it). Anyways, I got it at this place in Dietikon- they have a website though I haven't had a look at it- www.balteschwiler.ch. Don't know if it's exclusive to this wood flooring store or not. We also rented a machine there for more intensive cleaning.
I don't think it's such a good idea to sand the floors- they're not thick wood like the kind of hardwood floors you might know from North America. Here, it's really just a thin layer. You can get some floor boards replaced (expensive though)- but a certain amount of wear and tear is surely acceptable from a rented apartment.

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Everything I've read on EF would seem to suggest not! Thank-you for the tip on cleaning, I have been looking for something to try.