Wipe the caps of the portobello mushrooms with a damp paper towel to remove any dirt. Remove the stems and discard. Scrape the gills from the underside of the mushroom caps and discard. Slice into ½ inch slices.
Mince two of the garlic cloves.
In a large bowl toss 2 tablespoons of oil, mushrooms, 2 chopped garlic cloves, the juice of ½ lemon, oregano, ½ teaspoon salt, garlic powder, onion powder, dried dill, marjoram, and ⅛ teaspoon of pepper. Add to a large frying pan on medium heat and cook and stir for about 10 minutes until the mushrooms are soft and have reduced in size.
Preheat the oven to 350 F.
Grate the cucumber with a box grater on the largest hole until you have 1 cup and slice the rest for topping the gyro. Add the cucumber pulp to a mesh bag or nut milk bag and squeeze out the extra water. Add the pulp to a bowl, and crush and add the remaining garlic clove, the remaining oil, Greek yogurt, fresh dill, remaining salt, remaining pepper, remaining lemon juice, and red wine vinegar.
Warm up the pita rounds in the oven for 2 minutes. Top with the cooked mushrooms, tomatoes, red onion, feta cheese, cucumber slices, and tzatziki sauce.