Thanks to all who contributed, especially with pointing out swarm vulnerabilities (Nifft) and using oil (Pell-Mell) and torches (Rystil Arden) as weapons.
I'm pretty sure that the party can handle them, especially with the abilities of the sword sage. She has both burning blade and another (shadow blade) maneuver that adds cold damage. (I would think that the cold damage should be just as effective as the fire damage from burning blade and both should follow the same guidelines as energy-enchanted weapons. Feel free to weigh in with dissenting or affirming opinions.) They should both work okay; she also has the feat that allows her to re-select her maneuvers as a full round action. The party also bought some oil flasks, so they should be able to inflict some damage that way.
I feel reasonably confident that the party will prevail. The swarm in question only deals 1d4 damage, so they should have some time with which to work.
Thanks again for helping me (and them) out. I'll keep checking back later, in case others have more tricks, tips, and information for me.