What are the stylistic techniques used by Washington Irving in his short stories "Rip Van Winkle" and "The Legend of Sleepy Hollow"?

There is something you could use in almost every paragraph of each one of these stories. Irving is a writer that uses a lot of imagery and poetic devices in his fiction. Both stories are loaded with metaphor, imagery, similes, hyperboles, etc. To get you started:

From The Legend of Sleepy Hollow:

Imagery:

Not far from this village, perhaps about two miles, there is a little valley or rather lap of land among high hills, which is one of the quietest places in the whole world. A small brook glides through it, with just murmur enough to lull one to repose; and the occasional whistle of a quail or tapping of a woodpecker is almost the only sound that ever breaks in upon the uniform tranquillity.

Notice the words the author uses to evoke the image of tranquility: "small brook glides through it" - "just a murmur enough" - "lull one to repose"

Imagery:

Some say that the place was bewitched by a High German doctor, during the early days of the settlement; others, that an old Indian chief, the prophet or wizard of his tribe, held his powwows there before the country was discovered by Master Hendrick Hudson. Certain it is, the place still continues under the sway of some witching power, that holds a spell over the minds of the good people, causing them to walk in a continual reverie. They are given to all kinds of marvellous beliefs, are subject to trances and visions, and frequently see strange sights, and hear music and voices in the air.

Notice the words that the author uses to evoke a mystical quality in describing Sleepy Hollow: "witching power" - "holds a spell over the minds" - "hear music and voices in the air". This imagery sets the stage for the story, which is going to be pretty spooky.

Simile, hyperbole, metaphor:

He was tall, but exceedingly lank, with narrow shoulders, long arms and legs, hands that dangled a mile out of his sleeves, feet that might have served for shovels, and his whole frame most loosely hung together. His head was small, and flat at top, with huge ears, large green glassy eyes, and a long snipe nose, so that it looked like a weather-cock perched upon his spindle neck to tell which way the wind blew.

This is the description of Ichabod Crane. The hyperbole is "hands that dangled a mile" - an exaggeration. The simile is his nose that "looked like a weather-cock" - the metaphor is "spindle neck" - comparing his neck to a spindle.

From Rip Van Winkle:

Metaphor, personification:

Whoever has made a voyage up the Hudson must remember the Kaatskill mountains. They are a dismembered branch of the great Appalachian family, and are seen away to the west of the river, swelling up to a noble height, and lording it over the surrounding country.

The metaphor is comparing the river to a "dismembered branch" - something "cut off". The personificatiobn is giving life to the river, i.e. "swelling up to a noble height and lording it over the surrounding country."

Similes:

He was generally seen trooping like a colt at his mother's heels, equipped in a pair of his father's cast-of galligaskins, which he had much ado to hold up with one hand, as a fine lady does her trian in bad weather.

Two similes; one comparing Rip's son to a colt and the other comparing his holding up his boots "like a fine lady".

Get the idea? You can read the text of both stories at the links below.