One of the big questions I had is whether or not evil spirits are able to hear our thoughts. Such an answer would be important for two reasons. First, if they can't hear our thoughts, then praying in my head, while useful and important to speak with my heavenly Father, is not a direct rebuke and confrontation of the evil spirit in my midst. To do battle, then, I should speak audibly. Second, if evil spirits cannot read my mind, then that may influence what I want to say out loud. There may be some fears and weaknesses I don't want to verbalize, which they could use to their advantage were they to know.
1) Like Dissolves Like: There is a general rule in chemistry about solvents, which is that likes tend to dissolve likes. This is why gasoline will dissolve petroleum based styrofoam (to make napalm), and why water will not dissolve oil (they are dissimilar in their structures). I would imagine there is a similar sort of generalization at play in our current discussion. If angels and demons are spirits, they don't communicate audibly in a physical manner. Physical noise is simply the disturbance of air created by our physical bodies - the physical acting upon the physical. But angels and demons are incorporeal and not material beings like us. They are moving all around us, and presumably communicating with each other, yet we don't hear it. Why don't we hear it? Because they are speaking acting in their form, not in the physical form.
Assuming that angels and demons are spirits of a similar sort to us, I wonder why these creatures which "live" and "breathe" in the incorporeal, spiritual realm and must be ultra-attuned to that realm cannot hear what our incorporeal spirit says. Assuming that this is what our minds and thoughts are - our spirit speaking - I don't know why one would think it absurd that angels and demons could hear our thoughts. This isn't just something you can dismiss lightly. One of the major Christian arguments against materialistic determinism is that thoughts are not merely chemical reactions, but the mind (or spirit or soul) acting on the brain. When one thinks, most Christians argue that this is the spirit in action. And if thinking is the spirit speaking, not mere chemical reactions, then why is it absurd to think that spiritual beings who speak and hear in spirit can hear our spirit's voice?
At least one alternative question then also arises, which is if demons and angels are spirit, then can they hear physical words? Anecdotally, it seems they can. However, the only examples I can think of in the Bible where angels and demons are seen conversing with humans is when those entities are either inhabiting humans or they have taken physical/humanoid form.
2) Demonic Inception: James makes it very clear that much of our sin is a result of our being pulled into evil by our own wicked desires. However, we do know that evil spirits are able to influence our emotions, thoughts, feelings, etc. Job gives us a vivid picture of the extent of Satan's power, as Satan influenced marauders to kill and plunder, controlled the weather, and had power over physical ailments. We further see the power of demons in the New Testament as they oppress and possess a number of individuals, inciting some to violence, some to speak, and some to apparent lunacy. One has to ask what it means for a demon to influence us. Clearly, it can mean it ails our body through Job's boils or through the demoniac's convulsions. But it also seems to mean that demons can implant or influence thoughts in our minds and they may be able to be a part of our inner voice, turning our monologue into a dialogue.
If it seems clear that demons can influence our internal components, why would we think it doesn't work the other way. If they have access to our spirit in some form, when our spirit acts, does it not then interact with them? When I speak, you can hear, and likewise, when you speak, I can hear. It tends to work that when a creature has an ability to be influenced by another creature, they also have the capability to influence the other creature in like manner.
3) Anecdotes: While I have only had one overt encounter with the demonic, we have spoken with many others who have had a variety of experiences with the demonic. In one of these stories, a woman was in a coma and having interactions with demons. The story is too long to get into, but due to our faith in this individual as well as some of its ability to be authenticated in a variety of ways from others, it seems that the woman who experienced this was genuinely conversing with demons in her mind (as it couldn't have been verbally since she was in a coma).
If her experience was real, then one has to ask how the demons could have had a conversation with her if one requires omniscience to hear someone's thoughts (or spirit). I guarantee you that if you find some stories of demonic influence and interaction with people, you will find more and more stories where demonic access to our spirit's voice (our thoughts) is the only way to make sense of some of these stories.
Conclusion: I don't know that this discussion matters much in terms of how I act. While I used to feel nervous about expressing certain thoughts and fears in our old house where we were being demonically oppressed, I suppose recognizing that the demons likely know my thoughts makes me more free to share with others out loud things I wouldn't want the demons to otherwise know. I also don't think this will make me confront the demonic any differently in terms of whether or not I do it in my head. We see Jesus vocally confront the demonic, and it certainly can't hurt for us to do that too - along with praying in our heads.
What I think this conversation can do, however, is to help us understand the potential power the demonic really does have. While we see the power of Satan to its full extent in Job, being reminded that the one who seeks to devour our souls (and his minions) may have tremendous power over us in terms of the knowledge they can use against us. This should drive us to guard our thoughts even more and to practice spiritual disciplines which produce lives lived in discipline and constant prayer.