The power dissipation of a resistor = I2R = (.02)2*55 = 0.022 Watts.Don't forget to take into account the tolerance of both the resistor and the 1.1V reference. The latter is around 10% for the ATmega328, so the actual value of the voltage reference could be as low as 1.0V. In that case, the 47 Ohm resistor is the best choice.
Now I'm looking at getting some 55 ohm resistors which will allow the 20mA to be converted much closer to 1.1V, which my inexperienced mind tells me I'd be getting the full range of 1024 steps out of the 1.1V, as opposed to the roughly 875 steps I can measure when using a 47 Ohm resistor, which will only give around 940mV at 20mA.
0.25 watt (sometimes called 0.4watt)
Rating is rating and nothing to do with size. If the manufacturer rates is at 0.25W then that's what it is.