Harry lost the connection to Voldemort when that piece of the soul was destroyed. He lost the ability to speak Parseltongue. Was Harry's connection to his wand still as strong even with the piece of Voldemort gone?
Yes, I believe that Harry's connection to his wand was still as strong as it was when he first purchased it at 11 years old.
In Deathly Hallows, you will remember that upon the escape from Godric's Hollow, Hermione cast a curse that rebounded and broke Harry's wand. They tried to repair the wand, to no avail, and even Ollivander, after his rescue from Malfoy Manor, tells Harry that his wand is beyond repair.
In the Battle of Hogwarts, Voldemort is using the Elder Wand (which we later find out has given its allegiance to Harry) and Harry is using Draco Malfoy's wand (taken from Draco during the Escape from Malfoy Manor), so therefore, the twin cores are rendered null and void as neither wizard is using one of the twin wands.
Harry, of course, wins the duel with old Voldemort in the Great Hall, and finally takes possession of the Elder Wand, that refused to do harm to Harry, due to its allegiance to Harry. Harry later uses the Elder Wand to repair his own wand that he has continued to carry, even though it has been declared non-mend-able by an expert in wandlore.
After Harry repairs its wand, it shoots out some sparks and Harry "knows" that his wand will work properly again. (I do not have the book with me to provide quotes)
I think for these reasons, it is a safe guess that when Harry was 11, in Ollivander's shop, the wand choose to give its allegiance to Harry, and not the part of Voldemort's soul that was living within Harry at the time.
Furthermore, it is unknown what effects repairing a broken wand would have on its allegiance to its owner, but given the circumstances, I would assume that the wand, to use human emotions, would be grateful for being repaired, thus strengthening its bond with Harry (no canon evidence for this, just a guess).
Yes, Harry’s bond with his wand seems still there after the battle.
The piece of the Dark Lord’s soul in Harry is killed when Harry’s hit with a Killing Curse, and he seems just as bonded with his wand after that. When he fixes his wand with the Elder Wand, he feels like his wand and his hand are rejoicing in their reunion.
“He laid the broken wand upon the Headmaster’s desk, touched it with the very tip of the Elder Wand and said, ‘Reparo.’
As his wand resealed, red sparks flew out of its end. Harry knew that he had succeeded. He picked up the holly and phoenix wand, and felt a sudden warmth in his fingers, as though wand and hand were rejoicing at their reunion.”
- Harry Potter and the Deathly Hallows, Chapter 36 (The Flaw in the Plan)
This indicates that Harry and his wand were still bonded when the piece of the Dark Lord’s soul was gone, since the piece of soul in him is gone and the Dark Lord died before then, and Harry’s wand still seems quite bonded to him though both the soul piece and Dark Lord are gone by then.
Also, there’s no reason it shouldn’t be - Harry hasn’t changed.
In addition to his wand clearly reacting in a way that indicates the bond between Harry and his wand is still there, there’s no reason why it shouldn’t be - Harry is still the same person he was when he got his wand. He’d had his wand for more than six years by then, so it’d have had time to connect with him, and become familiar with his personality and style of using magic.
“The best results, however, must always come where there is the strongest affinity between wizard and wand. These connections are complex. An initial attraction, and then a mutual quest for experience, the wand learning from the wizard, the wizard from the wand.”
- Harry Potter and the Deathly Hallows, Chapter 24 (The Wandmaker)
While he did have a piece of the Dark Lord’s soul in him both when he went to Ollivanders and his wand chose him, and for the years since then until it was killed, it didn’t affect who Harry was - he was the same person with or without the soul piece, it didn’t change his personality. When doing an interview, J.K. Rowling mentioned that Harry hadn’t been ‘contaminated’ by having it.
JKR: And so this part of it flies off, and attaches to the only living thing in the room. A part of it flees in the very-close-to-death limbo state that Voldemort then goes on and exists in. I suppose it’s very close to being a Horcrux, but Harry did not become an evil object. He didn’t have curses upon him that the other Horcruxes had. He himself was not contaminated by carrying this bit of parasitic soul. The only time he ever felt it stirring and moving was in Order of the Phoenix, when he himself goes through a very dark time.
- PotterCast (Dec 23, 2007)
When the piece of soul was removed, Harry’s personality wouldn’t change - he’d only lose the few abilities he had connected to its presence, like being able to speak Parseltongue. Therefore, Harry himself shouldn’t have changed in any way that’d make his wand suddenly lose its bond with him.
According to me, the wand didn't choose Harry just because of the Voldemort's soul within it.
Other wizards don't have any other different souls within them, still wands chooses them.
So, my thinking is that the wand was aligned to Harry and not Voldemort's soul. So the connection should be as strong as earlier.
Again, this is my opinion. I don't have any canon proof.