" she was one of the several children who were sold at the auction."
The main thought of the sentence is "She was - sold at the auction" not "several children who were sold at the auction" which would otherwise be a hanging sentence (sentences that doesn't sound quite complete).
The answer therefore is "she was one of the several children who was sold at the auction" (main sentence is in bold, the rest are only supporting the main sentence).
My preferred way of determining whether to use singular or plural is by isolating the subject... who are we really discussing here? is it the "several children" or is it "she"? once you have come up with your possible candidates, eliminate the others then try each of them, determine if they sound complete.
I am not a grammar person nor a native speaker and I find it hard to understand all the rules in a grammar book so I cant explain the rules per se. if I'm wrong, kindly send me a feedback. This is all a learning process to me. Thanks