Is Judas liable for his betrayal sin? In Luke we are told, 

Luke 22:3And Satan entered into Judas who was called Iscariot, belonging to the number of the twelve. 4And he went away and discussed with the chief priests and officers how he might betray Him to them.

So then, did Judas sin or was it Satan inside him sinning?

If a computer hacker uses my computer to comit a crime all liability falls on the hacker using my computer. In the same way Satan utilized Judas as a vessel. 

Did Judas have free will in this matter (elsewhere in the Bible it says “Resist Satan and he will flee from you”, does that apply here?)
Judas' moral state becomes clear with the later disclosure by John that Judas was stealing and, by that theft, was depriving others of much needed charitable contributions.This deliberate moral state - the repeated act of theft - needs to be considered in juxtaposition to the stated question, as it paved the way for Satan's entrance. 

Judas had not been resisting Satan over the matter of secret theft.

This paved the way for much greater sin, later. Then, Satan came in like a flood and took him over completely.


  Then saith one of his disciples, Judas Iscariot, Simon's son, which should betray him, Why was not this ointment sold for three hundred pence, and given to the poor? This he said, not that he cared for the poor; but because he was a thief, and had the bag, and bare what was put therein. John 12 5,6 KJV.


The covetousness is apparent, the very calculation of value (and lost revenue to the thief) gives him away. This precipitated something within him. Was his betrayal a matter of recuperating the lost opportunity ?

What a shocking state he was already in ! He is irked by the loving act of the woman who 'squandered' the treasure of the spice on Jesus, anointing him for his burial, which was the only preparation received since, later, the women who went to anoint him, found him already risen.

Those around Judas were involved in charitable works, and in devotion to the Lord. He was fixated with money.