We appreciate you reaching out about nutria management. Because nutria are so large, they are beyond the lift-abilities of all but the largest birds (eagles and occasionally great horned owls). Here https://www.dfw.state.or.us/wildlife/living_with/nutria.asp is some brief advice on effective management strategies for nutria, and I have attached a somewhat longer piece from WA state. 
As to owls, you're very likely to have Great horned owls, and depending on habitat around your home, could also have western screech, northern pygmy, northern saw-whet and/or spotted (or more likely barred owl now). The western screech and barn owls will (potentially) use boxes more readily than most species. However, the Cornell Lab of ornithology can provide a download of plans for a nest box suitable for great horned owls: https://nestwatch.org/learn/all-about-birdhouses/birds/great-horned-owl/