Finally found quick answers on CD Baby... With that basket of instrument names in hand, I can now go and expand my research. Core instruments include: (1) hajouj or gumbri, a 3-stringed bass of the Moroccan Gnawa people; (2) duduk (doudouk), an Armenian double-reed; (3) kaval (Armenian/Turkish reed); (4) m'bira (sanza, or kalimba), or thumb pianos; (5) djembe (hand drum from Mali, Guinée, Senegambia, Ivory Coast (or Cote d'Ivoire), (6) hang drum; (7) bolong (bamboo wind instrument?); and more.
I wish it were easier to find the names of the traditional instruments they're using; I've scanned a pretty large number of Hadouk Trio's publicity pages, and so far...I'm not seeing full details. Okay. Guess I'll go search some more. Will find. Now 4:00 AM and cannot sleep until I know!