First, at the question : "do you really believe all of this ?" you can confidently answer "Yes". We can have faith in our faith, because it is utterly compatible with reason and science.
Regarding your question, I should decompose it in
1/ possibility of existence of such a thing as demonic possession
2/ necessity (or probability) of it happening
3/ spiritual meaning
If it is deemed not possible there must be some authority standpoint that says so. Logically we cannot rule out a possibility just because we did not witness it actualised.
So there should be a sound proof that it is not possible - or a sound belief that it is not possible.
The premise of rejection is a miscomprehension of science - which is widely believed to hold the truth about the universe in general and in all its aspects. Hence it is first necessary to return to actual science :
- modern science only emits hypotheses and temporary "best solutions"
To illustrate the point, this is why science could change radically (and several times) its view of the universe, life, existence of aethers, etc. For example, the existence of black holes is widely accepted as a scientific fact while no one has ever detected one.
True scientists remain aware that scientific "truth" is methodological, not actual.
So the possibility of existence of such a thing as demonic possession would actually be a valid scientific hypothesis. However, even with direct observations of the phenomenon in controlled environment, this could probably never turn into a science object.
The truth criterion in modern science is renewable material experience - same conditions, same results. So modern science is only capable of providing "truths" on material matters. There is absolutely no possibility (outside downright abuse of the science mantle) that science can bring freedom-related questions into its scope, and demonic possession is freedom-related (more accurately loss-of-freedom-related).
Side note : when science enquires the human mind it's often depressing because it only sees the mechanical part of our psychology. It is a built-in feature of science that it can only establish material causality - otherwise the best it can do is recognize that there is none (but this translate to "not a scientific fact").
- has not ruled out the existence of such things as demonic possession
- is intrinsically incapable of apprehending matters that are outside its (very efficient but very narrow) scope of material causality - so it won't ever rule on the question
You can only discuss such matters outside modern science - which does not mean outside reason or logic. So another step is to accept that it is possible to state something true about the universe (material or spiritual) outside the scope of modern science.
The scientific method is to remain logically consistent, establish some accepted principles that constrain the possibilities, and specify which kind of facts fall within the scope of the questionning. Different sciences can exist, leading to knowledge of different natures.
2/ Necessity / probability
Anthropology for instance is a field that brings a lot of knowledge, none of it being hard science. Through observation of customs, the belief in universal patterns and structures (family etc.), anthropologists have brought some useful self-knowledge.
I mention anthropology because all primitive cultures have spontaneously fostered belief in the invisible world. If it was an error, then it should happen in some specific cultures- why all of them ?
The christian faith is not an explanation of the material world, nor of our social world, but the tale of a relationship between Man and God, which existence we know indirectly
- through the testimony of saints, first of all Jesus,
- through intuition that we get contemplating life, nature, the universe etc.
Theology is the science of this relationship. Instead of renewable experience, the truth criterion is the scriptures, which hold both testimonies and intuitions. Those scriptures have not been randomly put on paper: wisdom accumulated, meditated and worked upon for centuries, starting with the intuition that God is.
Demonic possession would not be mentionned so clearly and repeatedly in the Gospel, especially as a subject upon which Jesus acts, if it wasn't essential to our understanding of redemption.
So the existence of demonic possession is not necessary per se (it is wrong), but you have to admit its reality in order to fully understand the Gospel. Nothing happens by chance in the life of Jesus, as showed by that in these occasions Jesus always frees people.
3/ Spiritual sense and return to everyday life
So the reality of demonic possesion is a loss of freedom through sin. Sin makes us slaves, incapable of achieving what we really want because we find ourselves following our "inclinations".
Every sin is a step toward possesion, and it manifests itself as such in its consequence, a greater difficulty to resist it. Finally some people find themselves unable to resist pulses that can lead them to outright horrors - but this was slowly built by progressive consent.
This is a reassuring psycho-fuzzy explanation, no longer is the demon needed...
But if you believe that the demon exists (if not please run a consistency check on your beliefs), there is no reason to reject demonic possession as the ultimate loss of freedom down the road of sin.
Actually it gives an account of our freedom, which goes so far as to make us able to rebuke God in everything he gave us, here the soul as the unity of body and mind.