In reply to Baron Weasel:
Are you planning to paint over them and are you filling to eliminate draughts or just for the look?
If painting then decorators caulk is easy to work with, paintable and reasonably flexible. No sanding needed, just a wet finger and a wipe with a wet cloth to remove the excess.
If you want to stop draughts while still being able to lift them for access I'd glue thin strips of wood to the underside of the boards along the edges where the tongue has been ripped off (notch the strip to clear joists).
I wouldn't inject PU glue, it's relatively expensive, messy and unnecessary.
jk
Post edited at 12:28