How did the curved blades such as damascus steel blades used during the crusades have any effect against Crusader and Western armor that was intended to protect against slashing blows?

It's very difficult to say definitively what the effect of Muslim blades on European armor was, precisely because no one really saw fit to write it down. Both Muslim and European chroniclers record the difficulty arrows had in penetrating European mail and padded armor, but to my knowledge no one ever particularly focused on one group's swords versus another. However, heavily armored Europeans seem to have been able, all other things being equal, to out-muscle lighter Arab troops in a stand-up fight. Based on this, I'm willing to speculate that the differences in sword technology were neither dramatic nor particularly important. At the end of the day, anyone trying to carve through mail, especially mail backed by a thick layer of padding, with a sword is going to have a very bad time of it. The Europeans, who seem to have preferred to armor themselves more heavily (at least their elite troops, who by c. 1200 were virtually protected from head to foot by mail), would probably fair better in a protracted melee, not because their swords were superior, but because they were using essentially equivalent swords against (generally) more lightly armored adversaries.