In order to study anything using the scientific method, it must be something that can be observed with your senses and that can be examined by formulating a possible causal explanation (hypothesis) for those observations. You must be able to test that hypothesis by designing an experiment that will either prove or disprove it. If the hypothesis is not supported by the results of your experiment, it will have to be modified and tested further.
As I tell my General Biology students, matters of faith and belief (which would include demonology) cannot be tested by the scientific method. I believe in God and the spiritual realm (including demons) because "the Bible tells me so", not because they can be explained by the scientific method.