Don’t worry about your English. I know one English person who doesn’t write it anywhere nearly as good as you do (and he’s distantly related to me by marriage 
)
Probably, what you read was “The emonTx cannot measure 3 phase voltages.” That is because it was designed only for the domestic UK system, which is almost exclusively single phase.
I have to say this: Never under any circumstances should anyone copy this unless they are qualified and experienced in working on live equipment, and fully understand the dangers.
As you’ve said, if everything is done very carefully… That is a very big IF. It is not just you who has to do everything correctly - what if there is a fault in your electricity supply? It’s quite possible that everything will then become live.
I would need a complete circuit diagram to give a definite answer that. My guess is the disconnected phase measures 3 V because it is measuring noise, very possibly coming from your switched-mode power supply.
Do you have a 4-wire system (L1 - L2 - L3 - N) or a 3-wire (L1 - L2 - L3), not counting the protective earth?
Is your star point (the junction of the three 1 kΩ resistors and the “GND” for your ADC) connected to the neutral of your supply system? If it is not, then the reason the other two phases read about 100 V is simple:
Your phase voltage is 120 V, therefore your phase-phase voltage is 120 × √3 = 208 V.
Your star point is on a voltage divider made up of 4 resistors ( 100 kΩ - 1 kΩ - 1 kΩ - 100 kΩ ) so it sits exactly mid-way between the two lines.
Each input then measures 208 ÷ 2 = 104 V.