Up to 4 hours ahead, prepare the vegetables and turkey for cooking.
Rinse turkey breast and pat dry. Make a lengthwise cut about 2/3 through the thickest part of the breast. Pat out meat to make evenly thick. If still uneven, make more cuts parallel to first, through thickest parts, and again press to flatten turkey.
To make sauce, mix orange juice, lemon juice, pepper, garlic, and 1 teaspoon salt. Mix 1/2 cup of the sauce with oil; cover and chill remaining sauce.
In a bowl, coat turkey with 1/4 cup of the sauce with oil.
Peel and cut onions crosswise into 3/4-inch-thick slices. Cut oranges crosswise into 3/4-inch-thick slices. Discard ends. Thread onions through the width of the rounds onto thin metal skewers to hold them flat. Thread oranges the same way onto more skewers.
Stem and seed bell peppers; cut lengthwise into quarters.
Trim off zucchini ends, then cut squash in halves crosswise and lengthwise. Thread pieces lengthwise onto thin metal skewers.
Remove and discard husks and silk from corn. With a heavy knife, tapping with a mallet if needed, cut corn crosswise into 2-inch rounds.
Brush all vegetables and orange slices with remaining sauce with oil.
Place turkey, all the vegetables, and orange slices on a barbecue grill over a solid bed of hot coals or on a gas grill over high heat (you can hold your hand at grill level only 2 to 3 seconds). Close lid on gas grill.
Turn vegetables and orange slices, turning as needed to brown evenly, about 5 minutes for oranges, 10 to 12 minutes for vegetables. As done, transfer to a large platter.
Cook turkey, turning once, just until meat is 160° on a thermometer or white in center of thickest part (cut to test), 15 to 20 minutes.
Transfer turkey to platter. Cut meat into pieces and pull skewers from vegetables and oranges. Pour reserved sauce over foods on the platter; add salt to taste.