Prepare the vinaigrette: combine olive oil, lemon juice, red wine vinegar, garlic, Dijon, oregano, and black pepper in a jar; shake until emulsified.
Cook the orzo in a large pot of unsalted boiling water until al dente, 9–11 minutes.
Prep vegetables: halve tomatoes; slice cucumbers and olives; dice bell pepper; thinly slice red onion. Place tomatoes, cucumbers, bell pepper, olives, and red onion in a large mixing bowl. Reserve feta, mint, and parsley.
Drain orzo (do not rinse). Add hot orzo to the bowl, pour in about half the vinaigrette, and toss. Let stand 5 minutes to cool slightly.
Add chickpeas and the remaining vinaigrette; toss gently to coat.
Fold in feta, mint, and parsley (reserve a little for garnish). Rest 10 minutes at room temperature, garnish with the remaining herbs, and serve.