Place the squid, shrimp, lemon, oregano and parsley in a bowl and toss. Set aside.
Make the vinaigrette. Place the arugula and red onion in a large bowl and toss to combine. Set aside.
Heat a large pan over high heat. Add the olive oil. Add the squid and shrimp. Season with salt and black pepper. Cook for 3-4 minutes or until just cooked through. Remove from heat and immediately add to the bowl of arugula and red onion. Serve on individual plates with additional freshly ground black pepper sprinkled over the top.