When selling personal items, they are normally considered personal sales, not hobby income, unless you are selling regularly for profit. Taxes only apply if you sell them for more than you paid for them, known as capital gains.
If you don't have purchase records, use reasonable estimates based on the estimated cost (value) and when you bought them. Keep detailed information about how you estimated the cost. You are not taxed if you sell at a loss, but you cannot deduct the loss. Be prepared to report the sales; normally, eBay issues a Form 1099-K, which you can use to report the sale.
For more information, you can refer to the IRS guidelines on selling personal items and TurboTax's help article on reporting personal items sold.
