Arrange the strips in a 5-quart slow cooker.
In a small bowl, combine the bbq sauce, Italian dressing, brown sugar, and Worcestershire sauce; pour over strips. Toss to coat.
Cover and cook on low setting for 3 hours. (Exact time may vary slightly depending on individual crockpot settings.)
Meanwhile, in a medium bowl, combine mayonnaise, salt, black pepper, celery seed, garlic powder, onion powder, and apple cider vinegar. Stir until well blended. Add coleslaw mix and toss to coat. Cover and refrigerate.
When the cooking time is up, transfer the strips to a cutting board and use forks to shred them. Pile the shredded BBQ strips onto toasted buns, top with coleslaw, then serve.