How should I store vacuum-sealed sliced salami?
You can store the vacuum sealed bags in the refrigerator or the freezer.  It would have been better to leave the salami whole for long term storage, simply to reduce the impact of oxidation and flavor loss. The only other thing that changes with slicing is the potential that you contaminated it, either by touching it or because your equipment was not clean.   If this is the case, you will observe mold forming on the salami.  If that happens, discard.  Otherwise, the only worry you have is flavor loss.  Frozen, I would say you have several months.  Refrigerated, you'll experience flavor changes after a few weeks.