Volcanic ash is a totally different thing from fire ash. Volcanic ash is basically exploded bits of rock and glass distributed in fine particles by the wind. Fire ash, aka wood ash, is the products of combustion, namely the oxidation of carboniferous (mostly plant) material, plus human products like plastics. Volcanic ash has a lot of silicates in it (some forms more than others)... again, think rock, but finer. Wood ash has metal salts in a relative abundance that reflects their occurrence in plant matter. The number one component in wood ash is usually calcium carbonate or calcium oxide (which turns into calcium carbonate over time), followed by salts/oxides of other metals like potassium. There's not much silicon in the ash that's left over after plant material and wood has burned, compared to volcanic ash.
Not to be overly sciencey about this stuff but I think that difference does matter.
As for the original question of what to do after everything burns down, I don't see a great need to remove everything. 500 feet is pretty far for toxic burn products to travel in any great quantity unless there was a wind driving them that direction. A friend of mine swears by the use of ash from campfires in his garden, and his plants are pretty great. Wood ash will tend to raise the pH of the soil, which could be an issue. This effect will be both immediate (potassium hydroxide is very water soluble and will leach out in heavy rain) and longer term (calcium carbonate is not very water soluble, but the carbonate will tend to end up as bicarbonate in solution over time, as it does in groundwater for example).
If this were my mess to clean up, I would try to remove the ash where it is obviously piled up after something big and woody burnt down, and just mix the rest of it into the soil, maybe along with some fresh compost to help reduce the soil pH some. On the plus side, charcoal is a pretty good soil additive and has the potential to actually improve the soil if it's mixed in right.
