Mix olive oil, balsamic vinegar, oregano, salt and pepper in a small bowl.
Toast pine nuts in a hot, dry skillet until browned -- about 2 minutes. Set aside.
Place peppers on a hot grill, over the flame of a gas burner or under a broiler and char them very well, turning to char all sides until the peppers are completely blackened. Place in a bowl and cover with foil or cling wrap and let steam a few minutes to loosen the skins. When cool enough to handle, pull the tops out of the peppers and peel off the skin. Slice the peppers lengthwise and remove the seeds. Slice each pepper into about ½-inch slices lengthwise. Brush pepper slices with olive oil and vinegar mixture.
Brush olive oil vinegar mixture onto each slice of eggplant and onions. Over a hot grill or preheated grill pan, grill the eggplant and onion slices until charred on the outside and soft on the inside. As each slice is done, remove from grill and brush again with the olive oil vinegar mixture.
Toss arugula with the remaining olive oil vinegar mixture and place in a wide salad bowl. Layer on the eggplant slices, then the pepper slices and then the onions. Crumble goat cheese over the top of the salad. Sprinkle pine nuts over the top.