Poltergeists have an uncommon ability to throw several items at once, all at full force. If you've identified a Poltergeist, cover the area its in with plenty of props so it's always in range of something to throw as it roams around.
To increase the chance of it using its ability, keep the lights off (use firelights to conserve sanity if needed) and light smudge sticks every few minutes if you have them around.