The language Washington Irving uses in "The Devil and Tom Walker" allows readers to infer (make a knowledgeable guess) that the setting is sinister and possesses supernatural characteristics.
The Sinister Setting
The following textual quotes define the setting as sinister.
-thickly wooded swamp
-secretly, and at night
-winding several miles into the interior
All of the above illustrate the dangerous nature of the setting. Something which is secret, wooded, winding, and treacherous depicts a place which can be frightening and dangerous.
The Supernatural Setting
-stories handed down from the times of the Indian wars
-cloven skull, with an Indian tomahawk buried deep in it
-On the bark of the tree was scored the name of Deacon Peabody
All of the above illustrate that the swamp contains secrets of its own. Given the stereotypes which define swamps, readers most likely see this place as one which possesses ghosts. The carving on the trees, the skull, and the stories all join together to compound the supernatural overtone.