What is the cheapest/easiest/quickest/best way to digitize thousands of paper photos? I realize these four parameters may be mutually exclusive.

Check around your local walmart/target/walgreens etc, that have those photo labs/booths. Some have proper bulk photo scanners publicly available, and will (or you can) pass your photos through one and spit out a CD for fairly cheap (sub-$10 last I checked, but years ago).