Well, let's start with the basics...
Acts 19:15-16 ESV
But the evil spirit answered them, "Jesus I know, and Paul I recognize, but who are you?" And the man in whom was the evil spirit leaped on them, mastered all of them and overpowered them, so that they fled out of that house naked and wounded.
I think these two verses shed more light on evil spirits/demons more than any other. I assume you're familiar with Lot and the other narratives when Jesus encountered demons? As you can see, they are quite smart and strong. One of them is an easy match for seven men in Acts 19 who attempt to cast it out. Yet. with the name of Jesus in our hearts, we have power over them. The mistake the men made here is that they thought the name alone, sans their own belief, would cast the demon out. Hence the reason he asks who they are. The implication there is that the demons are quite well aware of those who can order them out and whom cannot.
Other details come to light about them. In the case of Legion you have a mass possession, meaning that they can effectively "combine forces" and strength. Here again we have supernatural strength attributed to them. Christ also is able to rebuke a demon that his disciples cannot, and he goes on to say that it takes greater faith. The disciples were capable is the implication, but it takes prayer and fasting.
Mark 5:5
And they came to Jesus and saw the demon-possessed man, the one who had had the legion, sitting there, clothed and in his right mind, and they were afraid.
The possessed are always described with words like fierce, terrible, etc. In fact, the people were afraid when this fierce man was quiet and reserved like a normal person. It seems like they could be so scary for the pagan faith that it was absolutely terrifying to see someone formerly like this now calm and normal. That's quite a statement on the degree to which these demons could influence things.
Which brings me to another detail. Many folks associate demon possession with things like the Exorcist movie and so on. As we've seen, supernatural and terrible strength can be part of this. However, there are other MO's and ultimately demons have the same purpose as Satan - to deceive. Any good Christian can put a stop to Satan's shenanigans, and his demons know that. Yet they can use their supernatural ability to do things that keep people in terror. Other things they can do include causing physical ailments like being unable to speak and having blindness as we see in Matthew 12:22. In the passage in Matthew 17:14-20 that I mentioned earlier, the possessed as epileptic episodes.
So, as you can see, demons can do quite a lot to keep people in check, but they do it by deceiving one way or another.
With all of this in mind, I'll finish up with the actual words used for demon. In the Old Testament, you have the Hebrew word
sa`iyr, which is basically our word
satyr . I believe that out of this word comes our major misconception about demons. We think they're hideous creations - witness the recent unnamed movie where they are all sorts of things in the previews. The thing is, this term hits at something much more important. The thing is, this term is taken from the root
sa`ar which means to bristle on one hand (in a terrible way) and then stormy and virtually chaotic on another. If you really get into deep study, you'll see a couple things about demons. They are first and foremost goats in one sense. This comes from the word sa'iyr because it's basically half-man, half-goat. Why goats? Remember how we are the sheep? Goats are a very similar animal, but they have horns which are a symbol of power. I mean, what are you more intimidated by: a charging sheep or a charging goat with his horns?
Number two, the hair connects them to other beasts, particularly found in Revelation. Hair here seems to be an indication of unnaturalness (for lack of a better term). This is a study I admittedly need to do, but it seems like being hairy is a major connotation of demons. It gives them a terrifying perspective, much like perhaps a grizzly bear or lion.
Last but not least, you further have the connotation of storminess. This would be yet another scary element for men and women. We know that throughout the Bible the forces of Satan are always chaos in one form or another. This goes back to the very beginning when the world that then was perished and Satan was in open rebellion.
For an outside link that I pretty much agree with (as far as characteristics of demons), you can check this link which helps document certain aspects: http://www.dianedew.com/satan.htm
