Brush both sides of each tortilla with oil, using 1 tablespoon of the oil. Cut the tortillas in half, then cut each half into 1/4-inch wide strips. Arrange the strips on a baking sheet, sprinkle with the salt, and bake until crisp and golden, about 12 minutes. Remove from oven and set aside.
Heat the remaining 1 teaspoons of oil in a large heavy skillet over medium heat. Add the onion and cook for 5 minutes, stirring occasionally, until onion is soft and translucent. Add the garlic, jalapeno, cumin, and oregano and cook for 1 minute more. Add the broth and tomatoes, bring to a boil, then reduce the heat to low and simmer for about 10 minutes. Stir in lime juice.
Remove the pan from the heat and puree with an immersion blender or in 2 batches in a regular blender until the soup lightens in color but chunks of tomato remain, about 30 seconds. Serve the soup topped with the tortilla strips, a dollop of sour cream, and a sprinkle of cilantro.