Place quartered pork shoulder, onion, garlic and salt in the base of a pressure cooker or crock pot. Cover pork with 3 inches of water.
If using a pressure cooker, seal lid and cook for 1 hour. Carefully release pressure and allow pot to cool for five minutes. If using a crock pot, cook on low for 8 hours or overnight.
For pickled onions, combine sliced onion, vinegar, water, and salt in a bowl and mix well. Let rest until ready to serve, at least 30 minutes.
Remove pork to a shallow bowl. Using two forks, shred pork finely, stabbing at the meat and pulling the forks away from each other.
Add barbeque sauce and mix well, adding a little of the cooking liquid if mixture is dry.
To assemble, place three tablespoon of meat in the center of each tortilla, top with a scattering pickled onions and a few radish slices; serve immediately.