In a large bowl, combine the first eight ingredients. Cover and refrigerate for at least 30 minutes. For mayonnaise spread, in a small bowl, combine the mayonnaise, mustard, onion, garlic and oregano; set aside.
Grill bread slices, uncovered, over medium-low heat for 1-2 minutes or until lightly toasted. Turn bread; spread with mayonnaise mixture. Grill 1-2 minutes longer or until bottoms of bread is toasted. Drain tomato mixture; spoon over tops.