What is the difference between aspirin, acetaminophen, ibuprofin and naxproxin?

[hajario]

They are the most common over the counter pain medications available. The last three are most commonly sold under the brand names Tylenol, Advil and Aleve respectively. (Excedrine is a mix of aspirin, aceteaminophen and caffeine.)

How do they work? Given how they work, what would be the best choice for a standard headache and what for sore muscles from, say, a workout?