You need to know what voltage your LED/resistor combination will be driven with.
Assuming it is the full 9V (6 x 1.5V AA cells) from the NXT, the calculation is:
LED has 3.2V across it, so there is 9-3.2 = 5.8V across the resistor.
R=V/I (Ohm's law)
P=I x V
P=0.02 x 5.8
You'll find 270 Ohm or 330 Ohm resistors easily (http://en.wikipedia.org/wiki/Preferred_number#E_series
), and I expect either would be fine. You can work out the exact current and power with those values easily enough from the equations above.
1/8 W (=0.125W) should be OK for power dissipation, though obviously 1/4 will be fine, and may make you feel that your design has more margin.
I haven't seen carbon resistors for years! I think metal-film types are generally better (stability, tolerance etc.)