1W is a bus so each sensor is "sitting" on 3 or 2 wires (VCC, DATA, GND). Vcc is optional. Google will find you lots of pictures. The best practise is to have cable without stubs as I wrote above "from one sensor to another".
Power consumption for 20 sensor would not exceeds 100mA. It is able sink directly from the Arduino but in dependance on use of other devices you can use external power.
In any case you should read the datasheet for DS18B20.