Catalyzes the oxidation of long-chain primary alcohols and the oxidation of S-(hydroxymethyl) glutathione. Also oxidizes long chain omega-hydroxy fatty acids, such as 20-HETE, producing both the intermediate aldehyde, 20-oxoarachidonate and the end product, a dicarboxylic acid, (5Z,8Z,11Z,14Z)-eicosatetraenedioate. Class-III ADH is remarkably ineffective in oxidizing ethanol. a primary alcohol + NAD(+) = an aldehyde + H(+) + NADH a secondary alcohol + NAD(+) = a ketone + H(+) + NADH NADP(+) + S-(hydroxymethyl)glutathione = H(+) + NADPH + S-formylglutathione NAD(+) + S-(hydroxymethyl)glutathione = H(+) + NADH + S-formylglutathione 20-oxo-(5Z,8Z,11Z,14Z)-eicosatetraenoate + H2O + NAD(+) = (5Z,8Z,11Z,14Z)-eicosatetraenedioate + 2 H(+) + NADH 20-hydroxy-(5Z,8Z,11Z,14Z)-eicosatetraenoate + NAD(+) = 20-oxo-(5Z,8Z,11Z,14Z)-eicosatetraenoate + H(+) + NADH Binds 2 Zn(2+) ions per subunit. Homodimer. Belongs to the zinc-containing alcohol dehydrogenase family. Class-III subfamily.