Cook chicken: Heat air fryer to 370°F. In shallow bowl, mix panko, oil, and ½ teaspoon each salt and pepper. Transfer to piece of foil, fold up sides to create shallow dish, and air-fry, stirring twice through, until crumbs are evenly golden brown, 5 to 7 minutes. Return to shallow bowl to cool slightly. Heat air fryer to 400°F.
Place flour in second shallow bowl and beat eggs in third shallow bowl. Season chicken with ⅛ teaspoon each salt and pepper. Working with 1 strip at a time, coat in flour, then egg, then in toasted panko, pressing gently to help adhere. Transfer to baking sheet.
Working in 3 batches, add coated chicken in single layer, leaving space around each strip. Air-fry, flipping after 6 minutes, until golden brown and crisp, 9 to 10 minutes total.
Meanwhile, make sauce: In small bowl, stir mayonnaise, barbecue sauce, mustard, honey, lemon juice, and vinegar. Serve with chicken strips.
