\$ V_o \$ in this simple circuit with 2 diodes and 3 batteries
Vo is the voltage on that node specifically. The voltage across the resistor will be 10-9-0.6 = 0.4V
The voltage Vo, which is the voltage in that node is going to be 9 + 0.6V = 9.6V.
As long as BAT3 has a greater voltage than BAT1 or BAT2 , the current will be being sourced, ie, leaving BAT3 towards the circuit.
If BAT1 is different of BAT2, the voltage Vo will be with the voltage of the less value betwenn BAT1 and BAT2 +0.6V. So if BAT2 = 6V and BAT1 = 9V, Vo will be 6+ 0.6V = 6.6V

If BAT3 = 5V the voltage in Vo will be 5V too, as there will be no voltage across R3 due to the fact the diodes will be reverse-biased, thus allowing no current to flow through them.