Volatile oils are just oil extracts from different parts of a plant or tree - like olive oil. They are used in insect repellents, perfumes, anti-inflammatory ointments, and so forth.
Depends on the plant. There are too many uses of volatile oils to mention.
A common examples are chamazulene (German chamomile), lavender, eucalyptus, menthol (mint), camphor, so on...you get the idea.
As a child, Tiger Balm was what we keep in the house for all sorts of ailments -from common colds, coughs, headaches, to muscle and join pain. There are many tiger balm products, most of them contain the following: menthol, carrier oil, clove bud oil, camphor, and mint oil. Below are a few links on Tiger Balm. The odor is extremely strong, but it's effective.
I took my 90 year old grandmother to visit my sister in Wisconsin. On the plane, she decided that she felt a bit dizzy, so she took out her Kwan Loong oil without hesitation and started applying it on her forehead. I could barely stand the odor and I felt bad for those around us. No one said anything, for which I was thoroughly grateful.
Here are a few links to tiger balm:
Kwan Loong oil - this is what I grew up with
White flower oil - this is what I grew up with
Livestrong.com- talks about the ingredients in greater detail
Thepracticalherbalist.com - how to make tiger balm at home