is not afraid to cross (though others are) on the way home. He behaves as if he is oblivious to its dangers, and seemingly ignores supernatural associations with the swamp that others repeat and take for truth:

...stories handed down from the times of the Indian wars, when it was asserted that the savages held incantations here and made sacrifices to the Evil Spirit.

The treacherous nature of the swamp might have reminded some readers of Jonathan Edwards' sermon "Sinners in the Hands of an Angry God." Edwards also describes a treacherous landscape that the foolish hop about on with no realization of how close they are to eternal hellfire.

Not surprisingly, it is in this unsettling place that Tom meets the devil himself. The devil comes disguised as a man, but he has "a pair of great red eyes." Further, he associates himself with the Indians who made sacrifices to the Evil Spirit, stating:

I am he to whom the red men consecrated this spot, and in honor of whom they now and then roasted a white man, by way of sweet-smelling sacrifice.

He also says he is the patron of the slave traders and the "grand master" of the witches.

Another supernatural element is the local Christian church, which Tom joins in an attempt to wriggle out of his bargain with the devil. Comically,

He became, therefore, all of a sudden, a violent church-goer. He prayed loudly and strenuously, as if heaven were to be taken by force of lungs...

The hardened Tom believes fully in the supernatural at this point in the story, both in the devil and in the church. Finally, there is implicit evidence of the supernatural at work in the fate of Tom Walker's money and goods:

In place of gold and silver, his iron chest was filled with chips and shavings; two skeletons lay in his stable instead of his half-starved horses.

As other contributors have already pointed out, the main supernatural element of "The Devil and Tom Walker" is the presence of the devil himself. One can further claim that the devil's presence might be said to imbue the entire swamp with a kind of supernatural quality (it definitely has an unnatural air of menace about it). Indeed, one of the more memorable invocations of the supernatural can be found with the devil's trees, which ultimately stand as representations for human beings. One tree, bearing the name of Crowninshield, is depicted as having recently been chopped down. Later, Tom will learn the news that Absalom Crowninshield had recently died. (One can infer from this that the death of the tree is closely connected with the death of Crowninshield himself.)

A second example, also relating to the devil, can be found in the devil's mark, which the devil presses on Tom's forehead. Consider how Washington Irving describes this mark, writing:

When Tom reached home he found the black print of a finger burned, as it were, into his forehead, which nothing could obliterate.

Finally, I'd suggest that the entire picture of colonial life as Washington Irving depicts it is one where supernatural forces seem to be present and active within the world. Perhaps the most memorable passage referring to this larger context of large scale supernatural activity can be found in the story's second to last paragraph:

The good people of Boston shook their heads and shrugged their shoulders, but had been so much accustomed to witches and goblins, and tricks of the devil, in all kinds of shapes, from the first settlement of the colony, that they were not so much horror-struck as might have been expected.

Thus, within this world he inhabits, Tom Walker's experience is not particularly extraordinary or shocking. Quite on the contrary, the supernatural appears to be a basic reality of life as people know it.

Probably the easiest supernatural element to discuss in this story is the very real presence of the Devil himself. Tom makes a deal with the Devil and is granted special privileges. Another supernatural element isn't quite as concrete. That would be God. As Tom grows older, he begins to worry about his eternal soul, so he turns to church attendance, Bible-reading, and prayer. Tom obviously believes that God the Father must be real, because he knows that the Devil is real. A third supernatural element can be found when Tom declares, "'The devil take me, if I have made a farthing!'" Immediately after that declaration there is a knock on his door. It is the Devil, and he has come to take Tom with him.  

Just then there were three loud knocks at the street door. He stepped out to see who was there. A black man was holding a black horse, which neighed and stamped with impatience.

The sudden appearance of the Devil at the door screams otherworldly powers. Plus, when the Devil does take him, his horse is sparking fire behind him. Marvel comics copied this same idea in their "Ghost Rider" comic.  

Away went Tom Walker, dashing down the streets, his white cap bobbing up and down, his morning-gown fluttering in the wind, and his steed striking fire out of the pavement at every bound.

Lastly, the final paragraph includes some supernatural suggestions. The area where Tom supposedly first made his deal is said to be haunted.  

The very hole under the oak-trees, whence he dug Kidd's money, is to be seen to this day; and the neighboring swamp and old Indian fort are often haunted in stormy nights by a figure on horseback, in morning-gown and white cap, which is doubtless the troubled spirit of the usurer.

The first supernatural element in the story would be the devil, himself.  His image cannot be explained with any scientific accounts, and his presence conjures up the image of "the other side."  Another supernatural element in the story is the climax.  When Tom speaks to God, begging him to be spared, it is almost as if God was listening and his response was the devil's presence at the door.  When Tom was picked up by the devil, it was in the dark knight, away from the perceptive eyes of others.  This is supernatural, in that it retains a sense of mystery and the unknown.  The ending of the story, when Tom's house is burned and his financial record are cinders also retains some element of the supernatural, something that cannot be explained or justified through rational thought.  The element of the unexplained pervades the story.