What damage type does the sword created via the spell, Force Sword, deal? Slashing? Force? Or some other unexplainable damage type?
The spell force sword at its lowest level creates a "+1 longsword of pure force… that you can wield or give to another creature like any other longsword." This means it deals the damage like any normal, similar weapon would, hence slashing damage. (That it deals slashing damage is actually important due to how Pathfinder treats damage reduction, which is different from its D&D 3.5e forebear.)
Although certainly some spells do deal force damage, force damage isn't typically a thing, force not being one of the five cardinal energy types (acid, cold, electricity, fire, and sonic). (A cleric can't cast the spell resist energy and pick force, for example.) Instead, force is typically used in spells' descriptors—as it is here—to indicate that such spells "affect incorporeal creatures normally."
Taken together, this means the +1 longsword (or better) spell effect that's created by the spell force sword deals magical slashing damage (to determine whether or not its damage bypasses a foe's DR), and, because the spell also has the descriptor force, the spell effect can be used to make attacks against and deals damage to incorporeal creatures as if they were creatures that didn't possess that subtype or special quality.