To destroy their nest, you need to use harpy traps that you need to craft.
Some of the dwarf blacksmiths sells the diagram: Haggard, the blacksmith's apprentice, and Earso. Thorak also sell the traps themselves so you don't have to waste the precious silver ore.
You will find the harpies at the quarry.
Set the traps on the ground and lure them over. They'll pick up the trap and fly it to their nest. This grants 4/7 progress.
Continue with the main quest (Hunting Magic). You will find the rest in the harpy caves, which is hard to miss.