Karen,
The nose strips your talking about work by increasing the width of the nostrils (by holding them open) thus reducing resistance to breathing in through the nose due to small air ways. The reason people say your suposed to breath through the nose is to warm the air as DD and SS say but also because the hairs in the nasal passages (there are microscopic ones further in as well as the ones we can see) help trap unwanted particles like dust etc. The idea is then to breath out through the mouth were the airways are larger and thus expel the air more effieciently. All this said, when we're all pounding round puffing like we need four extra lungs the most important thing is to get the air in by the fastest means possible! therefore don't worry about using your mouth for either in or out - as with most things what ever feels comfortable will work. So don't concentrate to hard on it and let your body find its own way.
Hope this helps
Jim