Do I need a resistor because P1 has strong Internal Pull-ups

There is difference between pull-up and series current limiting resistor.

You definitely need current limiting resistor in series with each LED.

And since there are 8 LEDs, I suggest not to drive them directly from port pins. Instead use some driver chip such as ULN2003A or 7407 buffer.

If you have to drive them directly, connect the cathodes to port pin, limit the current of each LED to about 2-4 ma (using suitable resistor, whose value will depend upon the voltage rating of your LED) and connect the anodes through these resistors to 5V.

This small value of current will just glow the LED, and you will not get a bright light. But it will be Ok, to see the value from ADC.

IA