Place the pork shoulder chunks in a slow cooker with the onion, garlic cloves, cumin, oregano, salt, pepper, and chicken broth. Cover and cook on low for 8 hours until the meat shreds easily with a fork.
Remove the pork from the slow cooker and shred it with two forks. Return the shredded meat to the juices in the slow cooker and stir to coat. Keep warm until ready to serve.
While the pork finishes cooking, combine the white rice and water in a medium pot. Bring to a boil, then reduce heat to low, cover, and simmer for 18 minutes until the rice is tender.
Fluff the cooked rice with a fork, then stir in the chopped cilantro and lime juice. Set aside.
Warm the black beans and corn in a small saucepan over medium heat for 5 minutes.
Divide the cilantro lime rice among four bowls. Top each bowl with shredded pork, black beans, corn, avocado slices, shredded cheddar cheese, and salsa.