Prepare the pork shoulder by trimming excess fat and cutting it into large chunks.
In a large bowl, combine the teriyaki sauce, garlic, and ginger.
Add the pork chunks to the bowl, coating them thoroughly with the sauce mixture.
Place the sliced onion and pineapple chunks in the bottom of the slow cooker.
Place the coated pork on top of the onion and pineapple layers.
Pour any remaining teriyaki sauce mixture over the pork in the slow cooker.
Cover and cook on low for 6 to 8 hours or high for 4 to 5 hours, until the pork is tender.
Once cooked, shred the pork with two forks and mix it with the sauce.
Serve hot, garnished with chopped green onions and sesame seeds if desired.