The stranger is the man in the yellow suit. He tells Winnie in Chapter Four that he is looking for a family.
The man lifted his eyebrows. "Oh," he said, "I'm looking for someone. A family."
The family that the man in the yellow suit is looking for is the Tuck family, but the stranger does not know who exactly they are. All that the man in the yellow suit knows is the story that his grandmother told him. That story was about a family that supposedly had the ability to live forever. They never changed.
"I was born west of here," he began, "and all the time I was growing up, my grandmother told me stories. They were wild, unbelievable stories, but I believed them. They involved a dear friend of my grandmother's who married into a very odd family. Married the older of two sons, and they had two children. It was after the children were born that she began to see that the family was odd. This friend of my grandmother's, she lived with her husband for twenty years, and strange to say, he never got any older. She did, but he didn't. And neither did his mother or his father or his brother."
The man in the yellow suit believes his grandmother's story, and he decides to devote his life to seeking out and finding this family. He knows the general area of where to begin looking based on his grandmother's information, and the man in the yellow suit also knows that a particular music box tune is associated with the immortal family. When the man arrives in Treegap, he hears the tune while talking to Winnie in Chapter Four. The man in the yellow suit wants to find out the secret to the Tuck family's immortality and sell it for a large profit.