Using a paring knife, remove the peel and white pith from the orange and tangerine. Working over a large bowl, carefully cut between the membranes to release the citrus segments, allowing them to fall into the bowl along with any juices. Add the avocado, onions, cilantro and lime zest and juice to the bowl with the citrus. Gently toss to mix. Season the salsa with salt and pepper.
In a large nonstick skillet, heat the oil over medium-high heat. Sprinkle the halibut liberally with salt and pepper. Add the halibut to the skillet and cook until golden brown and cooked through, 3 to 5 minutes per side. Transfer the halibut to serving plates, top with salsa and serve.