Mental illness and possession by demons is a very important issue for us in the church.  There is not much gathered together, but there is much data from the early church fathers.  Lets look at some sources that are quite interesting.

St. John Chyrsostom

Homily XLI. on Acts 19. 8, 9  This is a beautiful description of how the possessed can use their state as part of their salvation.

Let us see to it, lest we have a demon: let us examine ourselves strictly. More grievous than a demon is sin, for the demon makes men humble. See ye not those possessed with a demon, when they have recovered from the attack, how downcast they are, of how sad a countenance, how fraught with shame their faces are, how they have not even courage to look one in the face? See the strange inconsistency! While those are ashamed on account of the things they suffer, we are not ashamed on account of the things we do; while they are abashed being wronged, we are not abashed when doing wrong: and yet their condition is not a subject for shame, but for pity and tenderness and indulgence: nay, great is the admiration it calls for, and many the praises, when struggling against such a spirit, they bear all thankfully: whereas our condition in very deed is a subject for ridicule, for shame, for accusation, for correction, for punishment, for the worst of evils, for hell-fire; calling for no compassion whatever. Seest thou, that worse than a demon is sin? And those indeed, from the ills they suffer, reap a double profit: first, their being sobered and brought to more self-control; then, that having suffered here the chastisement of their own sins, they depart hence to their Master, purified. For indeed upon this we have often discoursed to you, that those who are punished here, if they bear it thankfully, may naturally be supposed to put away thereby many of their sins. Whereas from sins the mischief resulting is twofold; first, that we offend; secondly, that we become worse. Attend to what I say. Not this is the only injury we get from sin, that we commit a sin: but another and a worse is this, that our soul receives a habit. Just as it is in the case of the body—for it will be more plain when put in the form of an example—as he who has taken a fever has got harm not only in this respect, that he is sick, but also that after the sickness he is become weaker, even though he may return to health after a long disease: just so in the case of sin, though we may regain health, yet we are far from having the strength we need. For969 take the case of one who has been insolently abusive: does he not suffer his deserts for his abusive conduct? Aye, but there is another and a worse thing to rue (which is), that his soul is become more insensible to shame. For from each several sin that is committed, even after the sin has been done and has ceased, there remains a kind of venom instilled into our souls. Do you not hear people saying, when they are recovered from sickness, “I dare not drink water now?” And yet the man has regained his health: aye, but the disease has done him this harm also. And whereas those (possessed) persons, albeit suffering ill, are thankful, we, when faring well, blaspheme God, and think ourselves very ill used: for you will find more persons behaving thus in health and wealth than in poverty and sickness. For there stands the demon over (the possessed), like a very hangman, fierce, uttering many (menaces), even as a schoolmaster brandishing the lash, and not suffering them to give way to any laxity. And suppose that some are not at all brought to a sober mind, neither are these liable to punishment;970 no small thing this: even as fools, even as madmen and children, are not called to account, so neither are these: since for things that are done in a state of unconsciousness, none can be so merciless as to call the doers to account. Why then, in a far worse condition than those who are possessed of evil sprits are we that sin. We do not, indeed, foam at the mouth, nor distort our eyes, or throw about our hands convulsively; but as for this, would that we did it in our body and not in our soul! Will you that I show you a soul, foaming, filthy, and a distortion of the mind’s eyes? Think of those who are in a passion and drunken with rage; can any form be filthier than the words they discharge? In very deed it is like a sputtering of noisome slaver. And just as the possessed know none of those who are present, so neither do these. Their understanding darkened, their eyes distorted, they see not who is friend, who foe, who worthy of respect, who contemptible, but they see all alike without a difference. And then, do you not see them, how they tremble, just like those others? But they do not fall to the ground, say you? True, but their soul lies on the ground and falls there in convulsions: since had it stood upright, it would not have come into the condition it is in. Or think you not that it betokens a soul abjectly sprawling and lost to all self-possession, the things men can do and say when drunken with rage? There is also another form of madness worse than this. What may this be? When men cannot so much as suffer themselves to vent their anger, but instead of that nourish within their own bosoms, to their own proper hurt,971 as it were a very hangman with his lash, the rancorous remembrance of wrongs. For it is a bane to themselves first, the malice that they bear. To say nothing of the things to come, what torture, think you, must that man undergo in the scourging of his soul, as day by day he looks how he may avenge himself on his enemy? He chastises himself first, and suffers punishment, swelling (with suppressed passion), fighting against himself, setting himself on fire. For needs must the fire be always burning within thee: while raising the fever to such a height, and not suffering it to wane, thou thinkest thou art inflicting some evil on the other, whereas thou art wasting thyself, ever bearing about with thee a flame which is always at its height, and not letting thy soul have rest, but evermore being in a state of fury, and having thy thoughts in a turmoil and tempest. What is more grievous than this madness, to be always smarting with pain, and ever swelling and inflamed? For such are the souls of the resentful: when they see him on whom they wish to be revenged, straightway it is as if a blow were struck them: if they hear his voice, they cower and tremble: if they be on their bed, they picture to themselves numberless revenges, hanging, torturing that enemy of theirs: and if, beside all this, they see him also to be in renown, O! the misery they suffer! Forgive him the offence, and free thyself from the torment. Why continue always in a state of punishment, that thou mayest once punish him, and take thy revenge? Why establish for thyself a hectic disease?972 Why, when thy wrath would fain depart from thee, dost thou keep it back? Let it not remain until the evening, says Paul. (Eph. iv. 26.) For like some eating rot or moth, even so does it gnaw through the very root of our understanding. Why shut up a beast within thy bowels? Better a serpent or an adder to lie within thy heart, than anger and resentment: for those indeed would soon have done with us, but this remains forever fixing in us its fangs, instilling its poison, letting loose upon us an invading host of bitter thoughts. “That he should laugh me to scorn,” say you, “that he should despise me!”973 O wretched, miserable man, wouldest thou not be ridiculed by thy fellow-servant, and wouldest thou be hated by thy Master? Wouldest thou not be despised by thy fellow-servant, and despisest thou thy Master?