As far as I know, there is no site that you can sell your gift cards in exchange for BTC. Maybe you can cash them for fiat and then make a buy of
BTC, I can't think another way.
Using a
BTCATM, sure, but I have a feeling that the fees would make it a less than ideal option, and that's assuming OP is in an area where he could find one. There are plenty of them in countries like the US, but if you look at the map on
coinatmradar, they're very sparsely spread out in the rest of the world (for now, anyway).
Your best bet is to look for a "single buyer" to purchase all of those and pays you in a single transaction.
I agree, and I also agree that the Digital Goods section might be OP's best bet. Gift cards are bought and sold in that section all the time as far as I know, though I'd also warn OP to check out the trust page of anyone he's thinking of doing a deal with--and even then, I'd probably use an escrow.
Good luck, OP. You can find a way to exchange those gift cards if you're persistent enough. Just be careful of all the scammers here, because there are a
lot of them.