The only thing to do is put them in tester and see if they break down below say 100v.
The tester is generally called a zener tester.
Then you put them in a power supply and draw about 700mA to 1,00mA and see if they work for a few hours.
If they do, you can use them for a 1 amp power supply.
That's about all they are good for.
They are NOT Schottkey diodes.
It could be a Schottky diode they will usually have a lower forward voltage drop than the silicon diode. This depends on forward current obviously, or more accurately the current is dependant on applied voltage.
Only one problem I can see with this is if you have a low reverse breakdown diode that is not a zener how would you know? Are the zener testers clever enough to determine between zener breakdown and avalanche breakdown? I don't know.
It could be a silicon diode a 1N4001 with 100 uA of current give approx. 0.5 V but I would hope the DMM would pass enough current through the diode to bring it in to full conduction, but I am not going to assume anything here.
Pass 5 mA through the diode and measure it's voltage drop. If it's greater than 0.6 V then it's either a zener or silicon diode if the voltage stays at 0.5 V then it could be a Schottky diode.
So to determine if it is a Schottky or a zener then do as Colin has said and see where it breaks down. If it breaks down 5.6 Volts or bellow then pretty sure it will be a zener. If it breaks down up to 20 V then I think it's going to be difficult because after 5.6 Volts the zener has a positive temperature coefficient just like the avalanche effect. So using heating to see if the reverse current increases is going to be pointless.
One other method is say it has a breakdown of 20 V and you want to know if it's a zener or a Schottky, then apply 10 Volts to it limited by a 1K resistor and measure the current you get through the diode. If it's around 1 uA then it's more likely a Schlocky as they have terrible reverse leakage current. If it's say 200pA then it's more likely a zener.
This is only a rough guide but should help in trying to work out what diode it is.
Thanks
Adam