Pat the pork belly dry and cut into 1.5-inch pieces.
In a bowl, toss the pork with kosher salt, black pepper, ground cumin, and dried Mexican oregano until evenly coated.
Heat the neutral oil in a heavy pot or Dutch oven over medium-high heat until shimmering. Add the pork in a single layer and brown lightly on all sides, 6–8 minutes total.
Add the orange juice and water, scraping up any browned bits. Stir in the thickly sliced white onion, crushed garlic, and bay leaves. Bring to a gentle simmer.
Reduce heat to low, partially cover, and cook at a steady simmer 1.5–2 hours, turning the pieces occasionally, until the pork is very tender and the liquid has mostly evaporated, leaving rendered fat; the pork should yield easily when pierced.
Remove and discard the onion, garlic, and bay leaves. Increase heat to medium-high and let the pork fry in its own fat, stirring every 1–2 minutes, until edges are deep golden and crisp, 8–12 minutes.
Warm the corn tortillas in a dry skillet over medium heat until pliable and lightly spotted, 30–60 seconds per side. Stack and keep wrapped in a clean towel.
Prepare toppings: finely chop the white onion, chop the cilantro, thinly slice the radishes, cut the limes into wedges, and set out the salsa.
Assemble tacos by filling warm tortillas with crispy pork belly and topping with onion, cilantro, and radishes. Serve immediately.