Can I use a single resistor for multiple LED with different +ve sources?
You can do that safely if:
- Only one LED is on at a time.
- The voltage of the circuit is less than the maximum reverse voltage of the LEDs. This often isn't specified by 5 V is generally quite safe.
Otherwise switching two or more on at a time connects them in parallel. In this situation the one with the lowest forward voltage will pass the most current. If they are different colour LEDs then the one with the lowest forward voltage, Vf, will be quite bright and the others relatively dim.
Figure 1. Variations in Vf with different colours of LEDs. Source: LED I-V curves.
Figure 2. Variations in Vf for the same type of LED due to variations in manufacture. Source: Variations in Vf and binning.
As you reminded me in the comments, I forgot to cover the current sharing aspect. The voltage at the top of R1 will be reasonably constant (because the voltage drop across the LEDs would be reasonably similar) so the current through R1 will be constant if one or more LEDs is on. That means that the current will be shared between the LEDs - fairly evenly if they're all the same colour but not so evenly if not.
It's problematic because nothing is ever identical so the LED with the lowest voltage drop will cause all the current to flow through it while the other two LEDs never turn on because the voltage drop across them isn't high enough.