Rinse quinoa under cold water. Combine quinoa and water in a saucepan, bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes until liquid is absorbed. Fluff with a fork and set aside to cool.
Season salmon fillets with salt and pepper. Heat 1 tablespoon of olive oil in a non-stick skillet over medium-high heat. Sear salmon for 4-5 minutes per side until the internal temperature reaches 145°F (63°C).
Remove salmon from heat, let rest for 3 minutes, then flake into large pieces with a fork.
In a small bowl, whisk together the remaining 2 tablespoons of olive oil, lemon juice, dried oregano, salt, and pepper to create the dressing.
In a large mixing bowl, combine the cooked quinoa, diced cucumber, halved cherry tomatoes, sliced olives, red onion, and chopped parsley.
Gently fold the flaked salmon and crumbled feta into the quinoa mixture.
Drizzle the dressing over the salad and toss lightly to combine. Serve at room temperature or chilled.