In a large bowl, mix together the mayonnaise, garlic, sweet pickle relish, onion, and red wine vinegar. For best results, refrigerate for 1 hour before serving.
Preheat grill and add oil to grill. Season shrimp with Cajun seasoning and add to grill in a single layer. Cook for about 2 minutes per side, until shrimp are done and turn opaque. Remove from grill immediately and set aside.
Spread tartar sauce on each side of each hoagie roll. Top with lettuce, tomato slices, onions, and pickles.
Divide shrimp evenly among the hoagie rolls.
Sprinkle with a little chopped parsley, if desired, and enjoy!