Trim any excessive thick fat from the pork shoulder and cut into large chunks.
In a small bowl, combine the dried oregano, ground cumin, garlic powder, onion powder, sea salt, and black pepper.
Rub the spice blend evenly over all sides of the pork pieces.
Place the seasoned pork into the slow cooker and pour the orange juice and lime juice over the top.
Cover and cook on low for 8 hours or on high for 4 to 5 hours until the meat is tender and easily falls apart with a fork.
Remove the pork from the slow cooker and shred using two forks, discarding any large pieces of fat.
To achieve the signature carnitas texture, heat a non-stick skillet over medium-high heat and add the shredded pork with a splash of the cooking liquid, searing until the edges are crispy and golden.
Warm the corn tortillas in a dry pan or over an open flame for 30 seconds per side.
Thinly slice the radishes and finely dice the red onion and cilantro.
Divide the crispy pork between the two tortillas and top with the onion, cilantro, and radish slices.