Wash all of the vegetables well.
Cut the peppers in fourths. Put in a big bowl.
Slice the zucchini and squash in half. Make 1/4 inch thick rectangular pieces. Don't cut them too thin or you won't get that meaty texture. Also don't cut them too thick or they will take much longer to grill than the rest of the vegetables. Add to big bowl.
Using a damp paper towel, remove the dirt on the mushrooms and add them to the bowl, whole.
Cut the tomatoes in half and add to the bowl.
Pour on the extra virgin olive oil, red wine vinegar, and dried oregano. Season with a generous amount of salt and pepper.
Toss well and let sit for at least 30 minutes to marinate.
Heat the grill to medium high heat.
Once the grill is hot, put each vegetable on individually. Don't pour the entire bowl onto the grill because it will flame up from the olive oil, and it's a hassle to move them around the grill. You may also lose some veggies through the grill grate if you do it this way.
After about 7 minutes, flip and grill for another 7 minutes, or until the vegetables are charred and cooked all the way through.
Transfer the vegetables to a serving platter and pour on some of the marinade that they were in previously.