Determine material of Zener's diode based on its characteristics
I'm not sure if I understand your problem, but if you want to determine which of the four types of diodes you have you can look at the forward voltage (V_f) and reverse voltage when diode starts to conduct at reverse polarity (V_r) and maybe reverse leakage current (I_rl) before that point:


Si-Diode: V_f ca. 0.6 V, large V_r, low Irl
Ge-Diode: V_f ca. 0.3V, relative large I_rl
LED: relative large V_f (> 1V, e.g. 1.4 V, depending on material)
Si-Zener-Diode: V_f ca. 0.6V, V_r = V_zener