We've just had a new oak front door and frame made and fitted and I spent a lot of time trying to decide how to finish it. I too wanted to try and keep the lovely honey tones of the natural wood, but eventaually came to the conclusion that it wasn't possible. After asking a lot of people the choice seemed to come down to either Danish Oil, and be prepared to re-apply at least once a year, perhaps more often, or a 2 part finish such as Sikens Cetol or Sadolin Classic + Extra.
The 2 part finishes are not available in clear as they rely on pigmentation to block UV light which causes as much damage as water, iand n the end I used the Sadolin "light oak" finish which hasn't changed the colour too much and I am pleased with the result, but only time will tell.
If you used something like the Sadolin light oak on your door it would probably hide a lot of the staining, especially if you rubbed it down first, however I am not sure how sucessful it would be on previosly oiled wood. The density of the grain means the oil wont have soaked in very far, but probably beyond "sanding depth". I wouldn't use linseed oil as this can leave a slightly sticky finish, although boiled linseed oil is better, and as Sgt Pluck says it would be best to leave it alone until they have been back to look at it.