We know that Voldemort had the exact same wand in book 4 that he had from his beginning into Hogwarts. Problem is, it seems like his wand is unaccounted for after the Potter's death until the end of book 4. What happened to the wand?
As per J. K. Rowling,
Wormtail, desperate to curry favour, salvaged it from the place it had fallen and carried it to him. I admit that would have been a bit of a feat for a rat, but they are highly intelligent creatures!
Source : Rowling's web chat transcript
Basically, Voldemort's wand was last seen at Godric's Hollow at the time that he died. Voldemort got his wand back in the summer of 1994 when Peter Pettigrew brought the wand with him after retrieving it from Godric's Hollow in order to gain his favor in exchange for protection.
Below I have expanded on the reasoning I have behind this point of view as well as providing the material I based my answer off of. I also provided a couple of reasons why I believe Voldemort's wand stayed at Godric's Hollow until it was found years later after Peter left to find Voldemort.
The following is a timeline of important events related to Peter bringing the wand to Voldemort. It also shows when the different deaths occurred using Voldemort's wand.
- 6 June 1994: Peter escaped from Hogwarts (Prisoner of Azkaban Page 452)
- Circa June 1994: Peter found Voldemort's wand at Godric's Hollow J.K. Rowling's Bloomsbury Live Chat Interview
- Circa Late June 1994: Peter brought the wand to Voldemort
- Circa July 1994: Peter found Bertha, bringing her to Voldemort. She had her mind searched and was killed afterward (Goblet of Fire Page 9)
- 19 August 1994: Frank Bryce died (Goblet of Fire Pages 11, 13-14)
The largest piece of evidence for when Voldemort possessed his wand is the spirit shadows that emerged out of his wand in the order that they were killed in as a result of the Priori Incantatem effect. Thus we know the order these people were killed was: Cedric Diggory, Frank Bryce, Bertha Jorkins, Lily Potter and James Potter (Goblet of Fire Pages 429-432).
The spirit shadows that appear from Voldemort's wand tells the reader that Voldemort had to have had his wand at the time the Potter's were killed and that the next time he had his wand was when Bertha Jorkins was killed. This means that Voldemort had to have had his wand as far back as July 1994. I don't believe that Voldemort had his wand before that since his defeat in 1981 reduced to "mere shadow and vapor". Voldemort told Harry that he has a form only when he shares another being's body (Sorcerer's Stone Page 236).
All of this leads me to believe that Voldemort was given his wand by Peter after he escaped Hogwarts and located Voldemort in Albania. One reason I don't believe Voldemort had the wand before this point is that he did not appear to use it when we saw him possessing Querril.
This leads to the question of how Voldemort got his wand back and where Peter got it from. The idea I believe is most likely is that Peter went to Godric's Hollow to get the wand in the summer of 1994.
When Wormtail escaped at the end of The Prisoners of Azkaban we see that he is extremely frightened that Sirus and Remus would kill him. I think this is the reason Peter chooses to return to Voldemort instead of hiding again. However, Peter knows that Voldemort would not be pleased that he hid away while doing nothing for so many years. This makes me believe that Peter would want to bring something that his master would value. In this case Voldemort's wand.
There are many possible places where Peter could have located the wand. However, the places I find to be the most likely are in the Ministry storage, in a place that Peter hid the wand, or it could have been left at Godric's Hollow.
To me, the Ministry of Magic feels like it would be too secure and possibly also hard to locate the exact place the wand could have been secured. As for the second possibility of Peter hiding Voldemort's wand; the main reason I doubt Peter hid Voldemort's wand before trying to run is that he was probably too scared of being caught by Sirus to consider that Voldemort's wand might be useful later.
So, this leaves Godric's Hollow as the last place I considered that Voldemort's wand would be found. Ordinarily, I would not consider this as a logical place to find Voldemort's wand since I would have thought the Ministry would have located it.
The reason I believe this to be the place Peter got the wand from is because of a quote made by J.K. Rowling in a live chat interview on Bloomsbury.com. As you can see below, J.K. Rowling states that Peter "salvaged [the wand] from the place it had fallen and carried it to [Voldemort]." This makes it sound very much like the wand was left at Godric's Hollow after Voldemort was defeated and never found until Peter came looking for it 13 years later.
Christiana: How did Voldemort get his wand back after he was in was exile?
J.K. Rowling: Wormtail, desperate to curry favour, salvaged it from the place it had fallen and carried it to him. I admit that would have been a bit of a feat for a rat, but they are highly intelligent creatures!
This is just speculation based on the events of the book: The last time he had a wand between books 1 and 4 was at the Potters'. Someone removed it from their house that night. I have a feeling Dumbledore would have wanted it, he would not have let the Ministry get their hands on it. He just needed someone to get it for him. My guess is Hagrid (as we already know he was there to get Harry) or possibly even Snape (If JKR intended him to be there like he was in the movie, she might have made them place him there for those scenes). They both would have given it to Dumbledore, who would have kept it hidden in plain sight at Hogwarts so on Voldemort's return he would have been able to get it. (He especially would have wanted Voldemort to get the exact same phoenix wand after Harry bought its brother) So I think that Wormtail, while he was wandering through Hogwarts during Ron and his brothers' school years, found it and hid it somewhere, realizing he could use it to get back Voldemort's protection. Then when he broke free from the Ron he took it to Voldemort.
Well remember, Wormtail was the Potter's secret keeper, he was the one to tell Voldemort where they were hiding so he was probably at the scene, maybe not in the house, but nearby. He probably heard what happened and went inside to check it out. I'm guessing he took it then and stashed it somewhere before Sirious Black caught up to him.
Many people say that Wormtail could have had it the 14 years, or may have gotten it later... sometime in the middle...
I agree that somebody had the wand, and the possibilities were Wormtail and Barty Jr... (since the rest of them didn't even know Voldemort was alive) But I think you were forgetting a very important "character" helping Voldemort at the beginning of book 4....
What if after Hagrid took Harry from the house, Nagini came in and kept the wand until it re-encounter his master... by the time Voldemort attacked harry for the first time, Voldemort had all the horrocruxes finished.
When Mrs. Rowling made her statement in 2007, she didn't say when Peter retrieved the wand. It makes much more sense to me that Peter just followed Voldemort to the Potter's home to see what would happen. Peter was not in any trouble at this time. When the place exploded Peter made his way in, found the wand, and took Voldemort's less-than ghost to the forest of Albania (Alba now Scotland). Peter knew where Voldemort and the wand was all along.
I absolutely agree with @dason's comment; what happens to the wand after Voldemort codswallops is still a mystery.
We can guess that Wormtail, Hagrid or Snape may have taken the wands. But Wormtail was busy running away from the scene, he created a fiasco and made Sirius go to Azkaban so I do not think he might have taken the wand then.
Hagrid and Snape both were in dilemma after the Potters were killed, so they might have not thought about Voldemort's wand either. And even if they would've picked his wand then there should've been some mentioning about it in the Chapter 'The boy who lived' from book 1, where Hagrid and Dumbledore meet for the first time after the attack.
Or if Snape had taken the wand then something should've been mentioned in Chapter 'The prince's memory' from book 7, where in the pensieve in Snapes memory, there's a scene when Snape comes running to see Dumbledore after Lily is killed. However, in both the cases nothing like that is mentioned.
The only possibility then left is that, Voldemort still possessed certain powers to retrieve his wand. Because it was also mentioned that he was possessing the body of other animals in the forest of Albania. If this required some kind of magic then it would mean that he still had the wand with him when he was in the forest of Albania.