Very loosely related (although a lot of the reasons given there don't apply here): Why didn't Bellatrix use Legilimency on Hermione?
Why did Voldemort torture Ollivander for information on the Elder Wand, given the existence of clear alternatives? There's a fair amount of evidence that torture tends to produce unreliable intelligence.
Why didn't he simpy use Legilimency on him to read his mind? I'm not aware of any evidence that Ollivander knew Occlumancy. Wouldn't that have been faster?
Couldn't he also have used Veritaserum? Based on the fact that he invented a potion to resurrect himself, he appeared to have been a skilled potion maker, so couldn't he have made it himself? He presumably could've asked Snape to brew it for him, too. I do recall the book saying that Veritaserum was a legally controlled substance, but that doesn't seem to have been much of an obstacle to him in other ways. Given that he had apparently read quite a few books in the Restricted Section of the Hogwarts library, it would be hard to believe that he had never encountered any information on how to make it himself. Given his propensity to manipulate others, this seems like exactly the kind of thing that Voldemort would want to know about.
Both of those methods would likely have been faster and (arguably) more reliable than torturing Ollivander.
So, why did he torture Ollivander?