There are some threads if you search here on the forum.
Often, if the stairs creak, it may be because the steps are glued in the stringers. New stairs that are screwed together become completely silent. I have read some thread suggesting you can drill small holes into the stringers and lubricate the steps, but I'm not sure if that works.
If your staircase is in varnished pine, I don't think you can oil it. We have renovated stairs at home by painting them white with regular lacquer and ordering new railings from a staircase supplier. They originally looked roughly like the picture you linked to. They became like brand new stairs after the renovation.