Okay, let's start here and pray it doesn't stir too huge a hornets nest in the thread.
The church word for demonic activity is demonized, this can come in two forms. 1. oppression. Oppression basically means that demons are attacking you from outside your being. It would be things like whispers in your ear, or personal attacks by others.
Here is an example. Right now, I am in a very serious situation in which someone very very close to me is contributing to abuse from people not as close to me. All of this is piled on previous abuses that I still battle daily. The end result is that I am fighting just not to give up, to just not give into to the self loathing and self inflicted harm that I can fall into easily. In fact, giving in means I stop studying scripture, stop praying, stop ministering, stop loving. In fact, I am so low today that it is taking everything to post this to you. That is because that is what Satan wants, he wants me to stop, to hate myself, to stop fellowship with God and delve into self doubts and hatred, pity etc. All people someone very close to me is adding more abuse to a situation that is already on the verge of all out abuse. That is oppression.
Oppression is fought by separating truth from lies and holding only to truth. It is fought by remaining faithful to God no matter the situation, which includes study of the word and prayer. It involves self inspection with honest eyes (which is my greatest difficulty right now) It involves telling Satan you are done with listening to the lies and that he has no place in your life. I could give a few others but that is the heart of it.
How you know whether or not it is oppression by asking God to reveal to you any area in your life that gives Satan a foothold For me it is self doubt, big time, and believing I have some worth at all, something redeemable about me. Be careful not to call everything an attack of satan, in fact the scriptures warn us about blaming demons for things they do not do. Rather search your life and search with God's help to see if there are areas that you are opening the door for Satan to do his work rather than closing those doors and allowing God to do His work in you.
The other possible is possession. From your posts I don't see evidence of this one, but posts are not always enough to know. Possession is attacks from within. This is a bit more difficult to deal with and would require someone that is Spirit filled to help you eradicate the demon/demons from your life. There is a biblical test for this one too, Scripture says that only by the HS can you confess that Jesus Christ is Lord!
Long story and I won't go into details here, but when I question whether or not I have given myself over to satan, I often simply proclaim out loud that Jesus Christ is Lord. You would be surprised by how many people I have given this test to and they have failed, they simply could not confess that Jesus IS LORD!
It is also helpful here to ask God to reveal, I have seen that work miracles as well, where something that was hidden in the darkness was revealed in the Light of God by simply asking.
Well, that is a start....again, Bondage Breaker is an excellent book that will help a lot to rid yourself of oppressions if they exist.
Oh, I forgot to mention and think maybe I should...open doors for demonic activities can be from the past or present. They can involve objects that have been brought into the house.
One such incident I encountered was with a young girl who was feeling convicted over some records she owned. God had been telling her to destroy them. I talked with her and encouraged her to follow God no matter the cost. She got so angry she pulled a knife on me and tried to stab me. But a force that she described as a hand, held her from stabbing me until she was ready to put the knife away. She burned those records and lets just say that the smell and flames were not normal, but had characteristics of demons.