Multiple the current for each diode by the number of diodes to get the required current. Add a percentage as you don't want to run at max. You already know the voltage.
Power in Watts is Current in Amps * Potential Difference in Volts.
That said surely this circuit consists of more than just the diodes ?
An advantage of wiring some in series is that you are then assured they are all (in each branch) carrying an equal current.
If you were to use a 24v supply, grouping the diodes into 20 parallel branches of four each in series with a 100 ohm (1/2 watt) resistor to help equalise the current in each branch, the total current supplied would then be 20 * 0.04 = 800ma.
As long as the supply is designed to provide the required current at the rated voltage, there should be no problem.