Lay the calamari tubes flat on a cutting board. Gently roll the top of the calamari one quarter turn and use a sharp knife to make slits from top to bottom along one side. This will help prevent the calamari from curling as it cooks.
In a bowl, combine the shrimp, calamari, 2 tablespoons olive oil, 2 cloves garlic, paprika, salt and pepper. Toss well to coat, cover and refrigerate 1 to 4 hours.
Preheat your Traeger grill to 500F (preheat to 475F if using the ModiFIRE Sear Grate). For gas or charcoal, preheat your grill to medium-high, direct heat.
Place the shrimp and calamari onto the grill and cook until grill marks form, 2 to 3 minutes. Flip and cook the other sides until grill marks form, the shrimp are pink on the outside and the calamari are opaque in the middle, 2 to 3 minutes. Transfer the shrimp and calamari to a serving platter and tent with foil to keep warm.
To a cold frying pan, add 2 tablespoons olive oil, shallot and 2 finely chopped garlic cloves. Place the pan over medium heat and cook, stirring, until the shallot is translucent and the garlic is fragrant, around 2 minutes. Add the capers, sundried tomatoes, sliced chiles and oregano and cook, stirring, 1 minute. Add the water and lemon juice and cook, stirring, until the liquid has reduced by ¼ in volume, around 2 minutes. Taste the sauce for seasoning and adjust with salt, pepper and lemon juice as desired.
Spoon the sauce over top of the shrimp and calamari and garnish with parsley. Serve immediately.