Figure out before you try to get rid of them which knickknacks and giveaways are actually special somehow. Take all the other ones, put them into bags, and take them down to the your local landfill for recycling. Now put the valuable ones on eBay, perhaps in one or more lots divided by brand. Not expecting to get any notable money, but that would be a nice side effect. It's just a nice way to handle getting paid for shipping, really.
Nobody wanted most of that shit when it was new. It has never ceased to amaze me how an industry which literally creates XL and 2XL customers will have 2000 size M tee shirts made, and 200 size XL, and 0 size 2XL. I've had to see some horrifyingly hairy midriffs in various technical departments.