I read somewhere that the mangaka made footnotes at the end of each volume explaining what inspired each story. I've only seen the anime so I would like to know which mythologies or folktales, if any, inspired the stories in Mushishi.
The author, Yuki Urushibara, does include authors notes at the end of each volume of the manga, explaining what inspired each story.
About "Heaven's Thread" she wrote:
"This is a story I thought of when reflecting on old folk tales my grandmother told me.Tales about how missing people were left upon a huge rock. There are similar folk tales all over, but most of them involve finding people in trees or on rooftops. They were usually blamed on Tengu or other spirits who abduct people."
About "A Banquet in the Farthest Field" she wrote:
"I lived in an apartment which looked out over an older brewery, and that became the model for this story. It had a nice atmosphere, but I had to move away, so now whenever I taste sake that's been strained through cloth, I get a very nostalgic feeling."
It was believed that in past times, it was common belief that spirits or demons caused sickness. This is even still true Western civilization, they say "bless you," because it was believed that in the a sneeze meant something evil was invading your body, so they would give a blessing to ward them off.
Some of the stories in Mushishi are based on old folklore, myths, and legends that the author heard growing up. Others, like the second story, were based on places she's seen or just a thought she had at the time and not really based on anything in particular. An example of this is the concept Second Eyelid the that appears throughout the story. I recommend purchasing the manga volumes when you have the chance, to enjoy these little snippets from the author and other stories not covered by the anime.
This essay provides a very good overview of concepts and themes of Shinto myths that inspired the manga:
In Shinto myth, the mysterious beings Blacker refers to are known as kami. Like mushi, they can be hard to define. Some people, quite specifically, believe kami to be beings from the other realm, while others, more generally, use the term to refer to anything beyond the ordinary...