To prepare pork, combine oregano, oil, salt, and pepper in a large bowl. Add pork; stir to coat. Cover and refrigerate for 2 hours. Thread pork and onion alternately onto 16 (8-inch) skewers.
Place skewers on a grill rack coated with cooking spray, and grill 14 minutes or until done, turning occasionally. Arrange skewers on a platter; keep warm.
To prepare sauce, combine guava paste and the remaining ingredients in a small saucepan. Bring to a simmer over medium heat; cook 8 minutes or until smooth, stirring constantly. Serve sauce with pork.