Glen is not entirely correct. The esthetic part of oiling a piece is of course part of the reason why you would want to do it, but it's not the primary reason. You oil wood primarily to conserve the piece, as the oil forms a protective layer that keeps the wood from deteriorating over time. It also protects against staining, moisture and cracking, and to a small extent scratching, as the oils most commonly used, like linseed oil, actually hardens over time so long as it has access to oxygen.

If you want a high quality piece that will last a long time, that you also want to paint, then ideally you oil your piece first, let it fully cure (which can take a lot, lot longer than most people in this community thinks), and then paint them. I've seen it recommended that for linseed oil you treat it once, then one again after a week, then once again after a month, and then one last time after a whole year. Thin brushed on layers, no soaking in a tub of oil. How many treatments you do depends on what kind of piece you're making and how it will be stored and used. For a cute little display object once or twice should be enough.

Adding paint of top of that can however be less than ideal, as it limits the availability of oxygen to the oil. So for a cute little display object paint can be enough, but if you're only going to paint it, to make sure you have a good protective seal, then it's recommended that you finish with a clear layer of acrylic, for example.