Soak 20 wooden skewers in water for about 20 minutes. Rinse the calamari tubes and pat dry. Split the bodies from top to bottom so you have 2 triangular pieces. Thread a soaked skewer through the length of each piece. Put the skewers on a platter and set aside. To make the vinaigrette, whisk together the oil, vinegar, garlic, dried and fresh oregano, thyme and lemon juice; season with salt and pepper. Pour 1/2 of the vinaigrette over the calamari; set the other 1/2 aside while you make the salad.
In a large bowl, add the tomatoes, onion, cucumber, cheese, olives, and romaine. Pour the remaining vinaigrette over the salad and toss to combine. Let marinate while you grill the calamari.
Heat the grill or a grill pan and oil it lightly. Grill the calamari for 2 minutes on each side, no longer or they will be tough. To serve, put the salad onto a large platter and top it with the calamari skewers. Garnish with fresh oregano leaves and lemon wedges.