Quick note: you go to this area multiple times. The first is when you eliminate high overseer campbell. The second is in the House of Pleasure quest where you rescue emily and eliminate two brothers that are fairly powerful. This is a guide for the second time you go there, the secrets and locations of the bone charms and runes are different each time you enter an area.
There are a few bone charms and runes around the place. There is one in Dr. Galvani’s house, 3 in the streets and apartments in the Distillery district and one inside the Distillery. There is also a secret where you help a woman escape from some guards.
To be able to complete this quest non lethally you have to complete the side quest. Its pretty straight forward, you have to go into Dr. Galvani’s house and find a dead guy.
If you have any trouble with the side quest or with finding the Bone Charms and Runes I suggest you watch the video below. I could describe it in words, but it is much easier to understand visually.