Each sword has five levels. You can upgrade them to level four using your orbs, but level five must be unlocked. Here are details for each sword :
Level 5 Oni Blade: Available after mission 8.
Level 5 Dual Blade : Unlocked after obtaining overal completion score A (no need for A+)
Level 5 Stonerender: Collect all shinobi moji, then restart mission 5. After the first boss and the "falling" sequence, you land in a big room. Head straight forward, then turn left in the opening in the wall. You'll see the sword. The level will finish at this point, after a QTE.