Rinse quinoa under cold water and drain well.
Combine quinoa, water, and 0.25 tsp salt in a medium saucepan and bring to a boil.
Reduce heat to low, cover, and simmer for 15 minutes or until liquid is fully absorbed.
Remove from heat and let quinoa rest covered for 5 minutes, then fluff with a fork and allow to cool to room temperature.
In a small bowl, whisk together olive oil, lemon juice, red wine vinegar, minced garlic, dried oregano, remaining salt, and black pepper until emulsified.
In a large mixing bowl, combine the cooled quinoa, cucumber, tomatoes, red onion, olives, and parsley.
Pour the dressing over the salad and toss to coat ingredients evenly.
Gently fold in the crumbled feta cheese immediately before service.