There are two widely available drying oils on the market that can be used as wood finishes: boiled linseed oil and 100% tung oil. Both dry to a non-sticky, very thin film after several days when all the excess is wiped off.
Here’s a comparison of the two oils.
Boiled linseed oil has driers added to make it dry much faster than raw linseed oil, which can take weeks or months to dry. The drying is adequate only when the excess is wiped off after each application. Tung oil doesn't contain driers. It takes two or three days to dry adequately in a warm room when all the excess is wiped off.
It usually takes four or five coats of tung oil, sanded after each, to get a nice even satin sheen. The surface will be rough and spotty until this point. That's why you have to sand.
Sanding is unnecessary with boiled linseed oil, except after the first coat. Then one or two more coats with a day between each will produce an even satin sheen.
The same number of coats of tung oil will be more water resistant than boiled linseed oil. In fact, boiled linseed oil won't be water resistant at all. The surface will dull after short contact with water.
Both oils will produce a slight orange (called “yellowing”) coloring, which will darken as the finish ages. The darkening occurs even inside the cans, so if your cans are old, you’ll notice that the finish is quite orange when viewed in a glass container. This isn't a problem, however, and both finishes are good until they gel badly in the can, which can take a very long time to happen.
Generally, I don't recommend using pure tung oil as a finish because of the difficulty applying it to an even sheen. But I know some woodturners who go to the trouble because they want the thin satin look with better water resistance.