Each has a huge number of meanings, which overlap. "Soil" emphasizes the substance, and the dirtiness. When I say "soil" I think of farming, seeds growing, earthworms... or dirty clothing. You can also use the word "earth" for this: "he dug up a shovelful of soil," "he dug up a shovelful of earth," but not "he dug up a shovelful of ground." "Ground" emphasizes what is underneath, what supports, what is below everything. "Her feet are firmly on the ground." "The open pit coal mine is a vast hole in the ground." "Earth" can also have this meaning. "Earth" tends to emphasize the planet as a whole. "In the old days they thought the earth was flat." You can't say "they thought the ground was flat," because "ground" just means whatever is nearby. The ground _can_ be flat, if it is not hilly or mountainous. You can't say "they thought the soil was flat," that makes no sense at all. But, yes, it can be a synonym for ground. In fact, in the context of electricity, in the U.S. we talk about a circuit being "grounded" while the British talk about it being "earthed!" With regard to dirtiness, you can say "the baby soiled his diaper" but you cannot say "the baby grounded his diaper" or "the baby earthed his diaper!"