In Goblet of Fire, Harry's and Voldemort's wands connect due to their twin cores, forcing Priori Incantatem to occur. Voldemort's wand spits out spectral figures of his last five victims. Later, after Harry is safe with Dumbledore again, Dumbledore explains that these spectral figures are not ghosts.
‘No spell can reawaken the dead,’ said Dumbledore heavily. ‘All that would have happened is a kind of reverse echo. A shadow of the living Cedric would have emerged from the wand ... am I correct, Harry?’
‘He spoke to me,’ Harry said. He was suddenly shaking again. ‘The ... the ghost Cedric, or whatever he was, spoke.’
‘An echo,’ said Dumbledore, ‘which retained Cedric’s appearance and character. I am guessing other such forms appeared ... less recent victims of Voldemort’s wand ...’
‘An old man,’ Harry said, his throat still constricted. ‘Bertha Jorkins. And ...’
‘Your parents?’ said Dumbledore quietly.
‘Yes,’ said Harry.
Goblet of Fire - pages 605-606 - Bloomsbury - chapter 36, The Parting of the Ways
Using Dumbledore's explanation, it seems these smokey figures should have emerged from Voldemort's wand, perhaps parroted back a few of the last sentences they said before dying, and then simply dissipated. The multiple definitions of 'echo' at Dictionary.com are not particularly helpful in working out a plausible definition of 'echo' that would explain these spectral figures.
I'm trying to figure out how these "echoes" could have possibly interacted in a sentient manner with Harry and had as much information as they did.
None of the figures who appeared knew that Harry's and Voldemort's wands had twin cores; they couldn't have anticipated Priori Incantatem. Bertha Jorkins calls Harry by name, even though she has never met Harry before. Lily tells Harry to "hold on", that James is on his way, and that James has been waiting to see Harry -- how could James's echo even know that Harry would even be there before James was out of the wand? James says, ‘[Y]ou must get to the Portkey, it will return you to Hogwarts ... do you understand, Harry?’ How did James's echo know about the Portkey at all, much less where it would transport Harry?
How were these echoes able to communicate effectively with Harry if they were not sentient ghosts? And how did they have so much information about Harry and what was going on at the moment of Priori Incantatem (i.e. like the Portkey)?