Toss the zucchini with olive oil and sprinkle with salt. Place the zucchini on the grill. Grill on both sides until the zucchini is soft, 4 to 5 minutes on each side.
Repeat this process with the onions, the onions will fall apart but don't worry about it. (Go ahead and fill up the grill with veggies!)
Repeat this process with the tomatoes, but only grill them for about 2 minutes on each side.
When all the veggies are grilled, cut the zucchini into 1/2-inch strips and toss into a bowl. Cut the tomatoes in half again lengthwise and toss them in with the other veggies. Coarsely chop the onions and toss them in with the others. Toss in the arugula and basil. Season the mix with salt and add the vinegar. Taste to make sure it is delicious, and adjust the seasoning, if needed.
Place on a serving platter and sprinkle with the feta.