I've noticed these things:
Every character is placed in a "skill family" job, like mason, carpenter, craftsdwarf, etc. based on their highest skill. Certain skills translate to certain jobs - for example, masonry and engraving are both in the mason jobtype. So, if a dwarf has Proficient engraving, he's a mason if every other skill is lower. Characters in a fey/secretive/possessed mood claim shops related to their job - Jewellers take jewel shops, Metalsmiths take forges/magma forges, etc.
For fey moods, and I think secretive moods, if the artifact is successfully completed the highest level skill in the current job is raised to legendary.
I find this hard to work around, since I like to use engraving as busywork for immigrants, which ends up with all of my strange moods going towards legendary engravers. I think if you want to try to focus your strange moods into skills that are very difficult to raise, like weapon/armorsmithing and so on, you really have to micromanage your guys to make sure they always have a top skill that won't inadvertently turn them into less useful legendary types like stonecrafters or engravers if their mood comes up. That's especially hard on immigrants, since they're only metalsmiths or carpenters based on a novice skill.
I've never seen two strange moods going on at once. I think it's an exclusive condition. They also don't seem to happen more often with a larger population, so I think the rate is flat rather than per capita, although the moods don't occur when the population is still less than 25 or so. Anyone disagree with that assessment?
An interesting strategy might be to try to load up on as many peasants as possible, get them to novice in a skill related to useful artifacts (ex: weaponsmith, bowyer) and then turn them into permanent haulers, sand collectors, or some other unskilled job. With enough of them, you're stacking the deck in favor of the most desirable artifacts and legendary skills in the Strange Mood lottery.