In a medium bowl combine all the dressing ingredients except for the oil. Slowly whisk in the oil.
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In another medium bowl add the calamari, salt, pepper, and 2 tablespoons of the dressing. Turn to coat, and marinate at room temperature for 15 to 30 minutes.
Prepare the grill for direct cooking over high heat (230° to 290°C).
Brush the cooking grates clean. Making two rows, place about 4 calamari tubes in a line over direct high heat so they can be weighted under the bricks. Place the bricks on top of the tubes with the smooth side of the foil facing down, close the lid, and grill until the tubes easily lift off the cooking grates, about 2 minutes. Wearing barbecue mitts and using tongs, carefully tilt the bricks onto their sides off of the tubes. Turn the tubes over, and set the bricks back in place over the tubes. Grlll for an additional 2 minutes. Transfer the tubes to a cutting board. Repeat with the remaining tubes, brushing the cooking grates clean after you remove the first batch. Grill the tentacles beside the bricks for about 4 minutes, turning once. Place on a platter. Cut the tubes crosswise into rings about 18 millimeters wide and add to the platter.
Put the tomatoes and onion into the bowl with the remaining dressing and toss to coat. Spoon the tomato mixture over the calamari and add the avocado. Sprinkle with the oregano. Serve warm.
