The Odd Old Man (real name: Archibald Paldock) starts the Rag and Bone Man quest and, afterwards, the Fur 'n' Seek quest. He collects bones, furs, teeth, and similar items for what was previously an unknown purpose. The bone sack on his back appears to talk to him and tell him what to say. He says he works for the Varrock museum, bringing stuffed creatures to put on display, but his phrasing suggests he is misleading the player, to hide the real reason why he wants these items.
After completing the wish list from the Fur 'n' Seek quest, it is revealed that the old man had found the remains of a powerful, undead, mind-controlling skeletal horror and carried them in the sack on his back for over 10 years. It is also revealed that he used the furs from Fur 'n' Seek to make himself a new outfit.
His real name, is most likely a reference to Captain Haddock (whose full name is Archibald Haddock) from the Tintin comic series. (Another character in this series keeps on misremembering his surname).
After completing the wish list following the Rag and Bone Man quest, the list will have "Non-chafing Manacles" written on it. After completing the Wishlist following the Fur 'n' Seek quest, you may speak to the Odd Old Man to get an explanation about this.
Also after completing the wishlist following the Fur 'n' Seek quest, the list will have "Nothing, actually" written on it.
The Odd Old Man's research is similar to the story of Frankenstein, in that both Victor Frankenstein and the Odd Old Man are consumed by their research to the point of committing atrocities by putting together monsters from dead body parts.
The Odd Old Man could be a reference to an urban legend about an escaped mental patient called 'The Body Dismemberer' who carried a large, lumpy bag. He would mutter to himself and claim that the bones in his bag "made him do it."
Fortunato appears to revere the man; when approached over buying vinegar, he becomes enraged at the thought he might carry it until you mention that you were sent to him. After learning that it was Paldock who sent you, he becomes highly respectful, and calls you "lordship" upon return trips.