Cut away peel and pith from 4 tangerines using a sharp paring knife. Slice each into 1/4-inch-thick rounds. Halve remaining tangerine, and squeeze juice into a large bowl. Whisk in oil, vinegar, and 1/4 teaspoon salt.
Mix together almonds, feta, and oregano.
Cut any large endive leaves in half length-wise. Add leaves to bowl with vinaigrette, and toss. Divide endive, tangerines, and almond-feta mixture evenly amound 4 plates.