How does shortage of oxygen halt the NADH dehydrogenase complex?
At a basic level this is quite straightforward if you look at an old-fashioned simplified diagram of the electron transport chain, such as the one below that I filched from the web.



If oxygen is absent then there will be a build up of the reduced forms of each cytochrome. Starting from the bottom, in the absence of oxygen cytochrome a is not reoxidized; if there is no oxidized cytochrome a then reduced cytochrome c cannot be reoxidized, and if there is no oxidized cytochrome c then cytochrome b cannot be reoxidized. The latter is the substrate of the NADH dehydrogenase complex — NADH-Coenzyme Q reductase in the figure — so this reaction stops for want of oxidised cytochrome b. 

(Years ago I demonstrated on a standard undergraduate laboratory class using rat liver (or perhaps beef liver) mitochondria, where you inhibited different stages and detected the reduced forms by their colours in the visible spectrum.)