Oil seeps into the wood and prevents water from penetrating. But, since it doesn’t completely keep water from touching the wood, it is prone to mildew.

If the wood is teak, it likely won’t require more than the oil, as teak has natural anti-mildew properties. Any other type of wood, I would consider a marine spar varnish.

Spar varnish is a thick sealing coat of urethane that they use on all exposed wood surfaces on boats. It comes in a gloss or satin finish, which both give the same amount of protection. The varnish is kind of an amber color and gives a deep luster to wood. It also tends to yellow a bit with age.

First, you should sand the furniture smooth to ensure a good finished surface. Use a tack cloth, or terry cloth damp with mineral spirits to clean off any sanding dust. When that dries, you can apply the varnish with an oil-based type of brush (these are more expensive, but they have the perfect bristle density for applying oil-based paints and varnishes). Put on a fairly thin, but even coat. You’ll be applying multiple coats to get it thick. But, if you try to get it thick in one coat, you’ll get lots of drips.

After the first coat, let it dry for at least 24 hours. If you don’t give it at least that much time between coats, the solvents in the next coat will dissolve some of the previous coat, causing blistering. And, the only way to fix that is to strip all the varnish off and start over.

Before applying the next coat, lightly sand with a fine grit (220 or higher) sand paper or with steel wool. This roughens up the surface a bit, so the next coat will stick better. Repeat as many times as necessary to get the surface finish completely covered (usually 2 or 3 coats will do).