For the salad: In a medium mixing bowl, combine the tomatoes, cucumbers, cabbage, lime juice and olive oil. Mix to combine and season with salt and pepper. Set aside.
For the tuna: Place the chiles, oregano, salt and pepper in a spice grinder or food processor and pulse into a coarse powder. Pour the rub into a glass baking dish. Add the tuna pieces into the chile rub and toss to coat. Set aside.
Heat 2 tablespoons olive oil in a large heavy saucepan over medium-high heat. Add the red onions to the pan and cook until softened and slightly browned, about 5 minutes. Season with salt and pepper. Remove the onions to a bowl and set aside. Into the same saute pan, heat the remaining 2 tablespoons olive oil and add the tuna pieces. Cook until no longer pink, about 5 minutes. Remove the tuna to a bowl and set aside.
To assemble the quesadillas: Drizzle the olive oil into the hot pan. Place a corn tortilla into the pan. Place 1/4 cup shredded cheese onto one half of the tortilla. Top with a spoonful of the tuna mixture and a couple slices of sauteed onion. Fold the bare half of the tortilla over, into a half-moon, and cook until the cheese melts and the tortilla forms a golden crust, about 2 minutes on each side. Remove the quesadilla onto a serving plate. Top with a spoonful of the cabbage salad. Repeat with the remaining 7 tortillas.