You have a good plan for your essay, and it is not surprising that you are struggling with the contradictory arguments to the existence of paranormal phenomena. The types of incidents, the consistency of them over time, and the sheer number of reported incidents is rather overwhelming evidence of paranormal activity.
A quick look at the research suggests two possible opposing points for your essay. First, scientists are not able to refine and highlight new effects of the phenomenon
[T]he data claiming to demonstrate paranormal events ''always stay at the very edge of perceptibility.'' As scientists learn more about a phenomenon, they can often refine their experiments to highlight the new effects. Despite years of work, that has not occurred with the paranormal research....
Second, paranormal activity is not scientifically reproducible.
Paranormal phenomena are usually not reliably reproducible. Thus one has reports of the events, but usually one does not have the ability to make the events recur at will. If paranormal phenomena were reliably reproducible, then it would be very difficult to say that they did not exist.
This seems to be the most effective argument: it cannot be verified scientifically, so there is the possibility, at least, that it is not real.
It is hard to discount so many people over so much time documenting these experiences (and discounting all of them as liars seems ridiculous), so your best strategy is probably to make the best contrary arguments you can and then move on to your position arguments. Happy writing!