When did Satan enter Judas: before the Last Supper or during it?

Both are right, because they describe two stages of Judas’s fall, and John himself mentions both. Luke 22:3 tells how, shortly before the feast, Satan entered Judas and he went to the chief priests to arrange the betrayal. John agrees that Satan was already at work in Judas before the supper: during it, he writes, “the devil having now put into the heart of Judas Iscariot” to betray Jesus (John 13:2; the Greek ēdē beblēkotos means he had already done so). Then, at the table, after Jesus had given Judas the morsel and so shown that he knew, “Satan entered into him” (John 13:27), and Judas went straight out to do it.

The same Greek verb (eiserchomai, ‘enter’) is used both times, but nothing in it means a single, once-for-all event: Satan could take hold of a man for his purposes more than once, first for the plotting and then for the deed. In the same way an evil spirit troubled Saul again and again (1 Samuel 16:14–23; 18:10). Barnes reads John this way: the devil had already put the plan into Judas’s heart, but at the supper Satan ‘now excited him to a more decided purpose’. Since John reports the earlier stage himself, he can hardly have meant to deny Luke’s account of it.

One process, two vantage points

Others read Luke 22:3 as a summary of Satan’s growing hold on Judas, told at the point where the plot began, which came to a head at the supper. On this view too Luke and John describe one process from different points in it.