Undead aren't immune to language-dependent spells (assuming they speak or at least understand the language; technically the skeleton and zombie templates at least don't lose their base languages, just those from int or linguistics), though they are immune to mind-affecting. Blistering invective only has the fire and language-dependent flags - you won't need threnodic spell to set a vampire spawn on fire with it. It's an evocation spell and not mind-affecting.
Edit: Intelligence as a nonability doesn't mention languages either.
A language-dependent spell uses intelligible language as a medium for communication. If the target cannot understand or cannot hear what the caster of a language-dependent spell says, the spell fails.
Mindless creatures usually cannot understand what the caster says, so blistering invective would not work on such creatures. In any case, I doubt mindless creatures can be demoralized, which is a prerequisite for the rest of the spell to work.
Besides, blistering invective does not have the mind-affecting descriptor, so it cannot be made threnodic in the first place. (It really should, though.)
Demoralize was at some point ruled to be a morale affect, IIRC correctly. Which Undead would normally be immune to. I would also say that mindless undead are immune to language dependent spells the way an animal would be.