Catalysis of the reactions: isocitrate + NAD+ = 2-oxoglutarate + CO2 + NADH, and (1R,2S)-1-hydroxybutane-1,2,4-tricarboxylate + NAD+ = 2-oxoadipate + CO2 + NADH + H+.
homoisocitrate-isocitrate dehydrogenase activity