Catalyzes the NAD-dependent oxidation and decarboxylation of (2R,3S)-homoisocitrate, (2R,3S)-homo(2)-isocitrate and (2R,3S)-homo(3)-isocitrate, into 2-oxoadipate, 2-oxopimelate (2-oxoheptanedioate), and 2-oxosuberate, respectively. All these substrates are intermediates in the biosynthesis of biotin and of 7-mercaptoheptanoate, a moiety of coenzyme B in methanoarchaea (PubMed:18765671, PubMed:10940051). Is also able to produce 2-oxoazelate from (2R,3S)-homo(4)-isocitrate in vitro, but this substrate is probably not physiologically relevant (PubMed:18765671). Is unable to use any isomer of isocitrate or isopropylmalate as a substrate, and NADP as an oxidant (PubMed:10940051). (2R,3S)-homoisocitrate + NAD(+) = 2-oxoadipate + CO2 + NADH (2R,3S)-iso(homo)2citrate + NAD(+) = 2-oxoheptanedioate + CO2 + NADH (2R,3S)-iso(homo)3citrate + NAD(+) = 2-oxosuberate + CO2 + NADH Binds 1 Mg(2+) ion per subunit. Stable at 100 degrees Celsius for 10 min. Organic acid metabolism; 2-oxosuberate biosynthesis. Belongs to the isocitrate and isopropylmalate dehydrogenases family.