For basic testing of an NPN silicon bipolar transistor with a DMM in diode mode:
Connect the base to + and the emitter to COM: display should be forward voltage drop, approx. 0.5V ... 0.7V
Repeat with collector connected to COM: about the same voltage.
Repeat both measurements with inverted polarity: reading should be overflow, displayed as OL or something similar.
If a transistor shows these results, it might still be damaged. But if it doesn't, it certainly is.
For PNP, the polarity of each measurement has to be inverted.
All this with the transistor connected only to the DMM. In-circuit is a different story.
Please note that OL is not 'not any reading', it's a measurement result. So if you see this and want to get help on what's going on, you help the helper if you write 'I get OL.'