Yes you can use 1 resistor for multiple LEDs. But if you want more than 1 LED at a time to appear on and keep the brightness levels the same, you must time-multiplex them; rapidly lighting one at a time so that one or more appear to be on together. Otherwise, the brightness will dim as the current allowed by the resistor is spread between the resistors.
If the LEDs are different colors, the LED with the lowest turn on voltage Vf (typically Red) will turn on and the LEDs with higher Vf will not turn on without multiplexing.