Is it permissible to make use of a room in the house, which used to cause disturbing dreams to whoever slept in it, after it was used for storage, given my need for it to study in preparation for exams?

There is no impediment to residing in the aforementioned room. The disturbing dreams experienced therein may not be due to ill omen or the presence of jinn. Regular adherence to the prescribed supplications in the Sunnah (definition)—morning and evening, after the five daily prayers, and before sleep—is sufficient to ward off any feared harm.