Current will start to flow when the anode is more +ve than the cathode by about 0.7v for a silicon diode.
Transistors junctions will test like 2 diodes using a ohm-meter on the diode test function. The common terminal will be the base, and from here you should get 2 diode readings, one to the emitter, and one to the collector. The one with the lowest reading (look carefully on the digital readout) will be the base-collector junction. You should get high resistance between collector-emitter. For NPN the "anode" side of the virtual diodes will be on the base and for PNP it will be the cathode.