Light a grill. Secure each onion slice on a toothpick. In a bowl, toss the onion and vegetables with the 1/4 cup of oil; season with salt and pepper. Brush the steaks with oil; season with salt and pepper. Grill the steaks over high heat, turning occasionally, about 8 minutes for medium-rare meat. Grill the vegetables, turning, until crisp-tender and charred in spots, 8 to 10 minutes.
Remove the toothpicks from the onion slices. In the large bowl, toss the vegetables with 1/2 cup of the olivada. Transfer the vegetables to plates and set the steaks alongside. Spoon the remaining 1/2 cup of olivada over the steaks and serve.