I believe that Washington Irving definitely creates an atmosphere of eeriness in "The Devil and Tom Walker." Here are some ways in which he achieves this.
Irving begins by detailing the swamp that dominates his story, and he describes it in detail: it is "thickly wooded" and features "a high ridge on which grow a few scattered oaks of great and immense size." When Walker goes into the swamp, Irving again takes pains to describe this gloomy and otherworldly setting. This extensive description is a critical tool for how Irving paints his setting, and it creates the atmosphere he is trying to convey.
In addition, there is the larger history of the swamp itself. As others have already said, even before Irving brings in Tom Walker and his family, he has already established something of the dangerous history of the swamp and its use by Captain Kidd to bury his treasure (under the watch of the Devil). However, Irving's backstory does not end there, for he also adds that shortly after burying that treasure, Kidd was actually captured at Boston and executed—an additional but noteworthy detail, in terms of the atmosphere this scene creates.
Irving adds supernatural elements with the presence of the Devil within the swamp and how he claims prior ownership to it, preceding the colonists altogether. There are also the trees, with names marked in them, each corresponding to a prominent member of the colony. Again, the description of the trees intensifies the atmosphere of eeriness and danger. Peabody's tree is described as "fair and flourishing without, but rotten at the core, and. . . nearly hewn through, so that the first high wind was likely to blow it down." There was also Crowinshield's tree, recently cut down, who Walker later finds out had only recently died. The description of the trees along with the Devil's words concerning the individuals in question, all within the context of a man later being discovered to have died, create a deeply otherworldly affect, especially when they are combined together.
Finally, as one last feature, there's the method in which the Devil departs. He descends into the swamp in a scene that has a deeply supernatural flavor to it. Irving describes it as follows:
So saying, he turned off among the thickets of the swamp, and seemed, as Tom said, to go down, down, down, into the earth, until nothing but his head and shoulders could be seen, and so on until he totally disappeared.