Oh dear!
Well, that does make things a bit trickier...
OK - if you haven't done so already, invite the landlady over and point out the musty smell. At the very least, you want to make sure you do not get blamed for any odor, mold or mildew that may result from this incident.
Let her know that IF the musty odor persists, or if you see the growth of mold or mildew....you will NEED to get a mold-remediation team out to check things for health reasons.
Meanwhile, yes run the fans and the de-humidifiers....but if there is mold growing within the walls, I don't think that will be enough!
I hope you can get this cleared up before anybody gets sick...