That woman could have been speaking in unknown tongues. I couldn't understand what she was saying but could tell it wasn't her normal voice. Most of the crazy people I dealt with were very strong though.Even for those that are trained in demology the differences between insanity and a demonic influence are subtile.
As has been mentioned on other threads, RCC exorcists are required to have the apparent demoniac go through psychological analysis before any attempt is made of actual exorcism.
The quickest test requires two people (and the subject). One should speak to and otherwise distract the subject while the other person (who has hidden a blessed object in his hand ) nonchalantly raises his hand with the blessed object behind the subjects head. If the person is possessed they will react strongly to the presence of the blessed object.
Other signs of true possession are aversion to the names of God, Jesus, Saints, etc., violent reaction to Holy Water, speaking in unknown tongues, inhuman strength, abnormal stenches from no source, and of course odd phenomena like levitation or stuff flying around of its' own accord.
It is a complex discussion.To what extent do you feel as a Christian that afflictions often attributed to demon attacks are psychological in nature instead?
How often do demons attack us?
I can't say for sure if I've ever seen one, but I'm convinced I felt one years ago when I was in high school. I am often reluctant to accept I've seen a felt something like that, but in this case, I really suspect I have.