In a large saucepan, cover potatoes with water and boil for 10-12 minutes. For the last 5 minutes of cooking, add the green beans and continue boiling until tender.
While potatoes are cooking, whisk together oil, vinegar, garlic and oregano in a small bowl; season with sea salt and pepper, to taste. Drain and rinse the potatoes and green beans with cool water, then toss with a few tablespoons of the dressing mixture. Set aside to cool.
Once the potatoes and green beans are cool, add the green onions, artichokes, olives and feta, along with the remaining dressing and toss to combine. Refrigerate and serve cool.