Preheat the oven to 400.
Add dried chiles to a pot of boiling water. Cover, remove from heat, and set aside for 30 minutes. Remove chiles from water, drain, and remove and discard stems. Add chiles to a blender with oil and salt, and blend on high for 2 minutes. Set a fine mesh strainer over a bowl and strain the chile oil; using a rubber spatula, press chiles to extract as much flavor as possible into the oil. Using a rubber spatula or a spoon, scrape fine bits adhering to the outside bottom of the strainer into the oil. Discard any skin and seeds remaining in strainer.
In another bowl, combine queso fresca, cotija, and half the queso quesadilla. Stir in onion, browned sausage, and the green chiles.
Working a few at a time, soften corn tortillas by dipping them in chile oil and then warming briefly in a small nonstick skillet. (This will allow them to be rolled without breaking.) Fill each tortilla with 1/4 cup cheese mixture and roll each filled tortilla into a tight cylinder. Place closely together in a 9-by-13-inch casserole dish, seam side down. Repeat until all of the filling and tortillas are used and pan is filled. Top enchiladas with remaining queso quesadilla and drizzle with a bit of remaining chile oil. Bake until heated through and cheese is melted, about 12 minutes.