I have looked into this same thing for myself but had no luck, most collectors wont look later then the mid 50s unless they are
Full Sets.
so the only way is to go through the piles and try posting them on ebay, which does have the potential to sell, but not as mixed lots you would need to list the valuable ones (which i have done and sold some cards like rookies and autographs successfully) and the rest can either a) get flushed b) use them as packing paper for the cards that do sell or c) wait until they are older but even then... also you might be able to dump them on a trader at a flea market but dont expect much.
PS if you do find a way to sell give me a pm so i can clean up my basement a bit also