To prepare pork, soak wood chunks in water about 16 hours; drain.
Combine paprika and next 6 ingredients (through dry mustard); reserve 1 tablespoon paprika mixture. Rub half of remaining paprika mixture onto pork. Place in a large zip-top plastic bag; seal and refrigerate overnight.
Remove pork from refrigerator; let stand at room temperature 30 minutes. Rub remaining half of paprika mixture onto pork.
Combine reserved 1 tablespoon paprika mixture, 1/3 cup vinegar, Worcestershire, oil, and beer in a small saucepan; cook over low heat 5 minutes or until warm.
Remove grill rack; set aside. Prepare grill for indirect grilling, heating one side to medium-low and leaving one side with no heat. Maintain temperature at 225°. Pierce bottom of a disposable aluminum foil pan several times with the tip of a knife. Place pan on heated side of grill; add half of wood chunks to pan. Place another disposable aluminum foil pan (do not pierce pan) on unheated side of grill. Pour 2 cups water in pan. Coat grill rack with cooking spray; place grill rack on grill.
Place pork on grill rack over foil pan on unheated side. Close lid; cook 4 1/2 hours or until a thermometer registers 170°, gently brushing pork with beer mixture every hour (avoid brushing off sugar mixture). Add additional wood chunks halfway during cooking time. Discard any remaining beer mixture.
Preheat oven to 250°.
Remove pork from grill. Wrap pork in several layers of aluminum foil, and place in a baking pan. Bake at 250° for 2 hours or until a thermometer registers 195°. Remove from oven. Let stand, still wrapped, 1 hour or until pork easily pulls apart. Unwrap pork; trim and discard fat. Shred pork with 2 forks.
While pork bakes, prepare slaw. Combine onion and next 5 ingredients (through 1/4 teaspoon salt) in a large bowl. Add cabbage, and toss to coat. Cover and chill 3 hours before serving. Serve pork and slaw on buns with Memphis Barbecue Sauce.