Preheat a grill to medium- high. Brush the tortillas with 1 1/2 tablespoons olive oil and sprinkle with salt. Toast on the grill until browned, about 5 minutes.
In a large bowl, toss the pork and onions with 1 1/2 tablespoons olive oil and season with the oregano, salt and pepper; thread onto 4 skewers.
Meanwhile, on a cutting board and using the flat side of a knife, mash the garlic and 1/2 teaspoon salt into a paste. Transfer to a small bowl and whisk in the yogurt, mint, remaining 1 tablespoon olive oil and 1/4 teaspoon pepper. Press the cucumber in a sieve to remove excess liquid, then stir the cucumber into the yogurt mixture.
Grill the skewers, turning occasionally, until lightly charred and cooked through, 8 to 10 minutes. Serve with the tzatziki and tortillas.