Oranges will last up to 2 weeks safely under refrigeration or out at room temperature. Do not stress over where you keep your oranges, the only key is to keep them in an open place. By covering oranges, you are eliminating air flow and enabling moisture to build up which is exactly what mold needs to grow.
Oranges are eaten fresh or juiced. Juice and/or zest can be kept longer but should be refrigerated. You can even freeze orange juice in a ice cube tray for easy smoothie work.