Irving does this in a number of ways.
First, I think you could say he does it with the epigram he uses. Invoking Woden (Odin) hints at paganism and the old days of Norse mythology. That makes us think there may be supernatural forces involved.
Then you can look at his description of the area. He talks about the "magical hue and shape" of the mountains that seem to change with every passing hour. He calls them "fairy mountains." Both of these lines indicate that there is something fundamentally flexible about the mountains -- that maybe they aren't solid and fixed like mundane reality is.
There is clearly a Romantic tone to Washington Irving's declared "folk tale," "Rip van Winkle." The description of the natural setting personified in imagery and other figurative language contributes to the mystery and magic of the Catskill Mountains:
When the weather is fair and settled they are clothes in blue and purple, and print their bold outlines on the clear evening sky; but sometimes, when the rest of the landscape is cloudless, they will gather a hood of gray vapors about their summits, which, in the last rays of the setting sun, will glow and light up like a crown of glory.
Because the Catskills (Kaatskills), having been personified as possessing powers themselves, seem capable of altering the forms of their nature. The allusion to the "crown" and the "majestic course" of these mountains creates the impression that they are above the natural order. Indeed, there is an other worldly quality to the elevated peaks that rise into the "azure sky" of the heavens.
Added to the Romantic descriptions of the mountains, Irving has created a frame around his story that emphasizes the truth of the tale, while distancing himself from accountability for the truth:
The following tale ws found among the papers of the late Diedrich Knickerbocker, and old gentleman of New York, who was very curious in the Dutch history of the province, and the manners of the descendants from its primitive settleers. His historical researches, however, did not lie so much among books, as among men....