Pat the short ribs dry and season all over with salt and pepper. Heat the oil in a large Dutch oven over medium-high heat. Working in batches, brown the short ribs on both sides, about 8 minutes total. Remove to a plate.
Meanwhile, combine the stock and dried chiles in a medium saucepan and bring to a simmer. Remove from the heat and let steep 15 minutes.
Discard all but 3 tablespoons oil from the Dutch oven. Add the onion and cook, stirring, until soft, about 5 minutes; add the garlic and cook 1 minutes. Pour in the red wine and port and simmer, stirring, until almost completely reduced, about 12 minutes. Add the chile-stock mixture: bring to a simmer and return the short ribs to the pot. Cover, transfer to the oven and cook until the meat is tender, about 2 hours, 30 minutes.
Remove the short ribs to a bowl; shred the meat from the bone. Strain the cooking liquid into a degreasing cup and pour off the excess fat. Pour the remaining liquid into a skillet and bring to a boil. Reduce to a simmer and cook, stirring occasionally, until thickened, 10 to 15 minutes; season with Tex-Mex. Return the short ribs to the pot and add the chorizo, toss to coat.
Fill the tortillas with the meat; top with salsa verde, pickled red onion and green chile relish.