Why is oxygen used up in eutrophication?
Algae produce O2 in the upper layer of water but when they die they stop producing O2. They sink to the seafloor and most get decomposed by bacteria on the seafloor. In this process, bacteria use O2 contained in the bottom layer of water which decreases the dissolved O2 concentration in the bottom water.

These concepts (and much more!) are well described in the excellent open-access paper by Rabalais et al. (2010) Dynamics and distribution of natural and human-caused hypoxia. It also includes case-studies of areas affected by hypoxia and eutrophication around the world. A must read if you're interested in this topic!