Does God control "demons"?

From a Catholic perspective:

I have a sense that there can be a distinction between the two. Namely, a demon is necessarily a fallen angel, while an evil spirit is any fallen spiritual entity. In my understanding, this can include dead, unrepentant humans.

That said, I would assume the scripture generally assumes an evil spirit is a demon. And, I would assume we can speak similarly about them, if not identically, for most purposes.

So, from the Catechism of the Catholic Church,

The Church teaches that Satan was at first a good angel, made by God: “The devil and the other demons were indeed created naturally good by God, but they became evil by their own doing.” ... The power of Satan is, nonetheless, not infinite. He is only a creature, powerful from the fact that he is pure spirit, but still a creature. He cannot prevent the building up of God’s reign. Although Satan may act in the world out of hatred for God and his kingdom in Christ Jesus, and although his action may cause grave injuries—of a spiritual nature and, indirectly, even of a physical nature—to each man and to society, the action is permitted by divine providence which with strength and gentleness guides human and cosmic history. It is a great mystery that providence should permit diabolical activity, but “we know that in everything God works for good with those who love him.”

You can find the scriptural references in the USCCB's online version of the Catechism, if you're interested.

So, everything in existence is subject to God's will. And all that occurs is, in the very least, occurring by His permissive will. That is, God does not plan the evil actions of the demons, but He sustains their existence and allows their free action: He wills their free will and action.

I would highly recommend the book God at War (see pages 80-81 specifically), written by Gregory Boyd, or this summary of it. It deals with this question as it discusses theodicy from the perspective of spiritual warfare. The author goes through the entire Bible, along with a number of other ancient texts, and demonstrates the constant theme of spiritual warfare, and places events such as Jesus' death, resurrection, and ascension into this context.

To answer your question from what I've learned in this book, I believe that God has delegated some of his authority to created agents with free will, both angels/demons and humans. God is sovereign, and could retake the authority at any time, but chooses instead to work within the rules that he himself has set up in order not to negate free will.

In this context, the demons sent from God were given a certain amount of limited authority, and were sent as judgment against Saul and Abimelech. The demons acted in an evil manner of their own accord, but God sent them specifically because they were evil.

So God doesn't "control" demons when it comes to them making moral decisions, but he does give them limited authority and places them in a limited universe with rules that he created.

No doubt God can rewind time and edit out anything He doesn't like, and we wouldn't even know about it. Having created time and being outside of it or inside it if He wishes He can do what He likes. In that way God can control demons if He likes or not as the case may be, plus He could change such later. There are no rules like "free will" for God otherwise God would be ruled rather than the ruler. Any human attempts to understand the workings of God must always fail hopelessly. There will surely be one million incredible different workings of God that we have no ideas of at all until such time as He reveals them individually to us.

There is no point whatsoever in using "references" for these kind of questions since anybody's opinion is as good as anyone else's. In short we know nothing and never will Earth side of Heaven. What is written in the Bible and other religious texts is a tiny piece of the whole, the most is hidden and secret of course.

As Zack stated, God is omnipotent, so He controls even demons. But demons (like all angels and human beings) have free will, so this control is limited. Jesus (or exorcists who act in name and authority of Jesus) casts out evil spirits "by the finger of God" (Luke 11:20) - so Father must have had authority to force the evil spirits to leave.

What you address here is the old Hebrews' understanding of God's omnipotence and of angels. In most of Old Testament, everything (good and evil) is attributed to God. Everything bad (including actions of evil spirits) was undrstood as God's way to punish the sinful. And the angels (including evil angels, demons) were not clearly distinguished from God Himself in older books of Old Testament. During Old Testament times, the understanding of both God's omnipotence (and free will of men and angels) and of the nature of angels has evolved. Book of Job is a sort of a polemic with the idea that everything bad is a punishment for sins, and Satan is first depicted as a cause of evil independent of God. God still has the final word, evil spirits can't do anything without God's approval. St Augustine wrote that if Devil was free to do anything he wanted, nobody would live. Why God don't stop many of evil spirits' plans? The answer is the same as for any other form of evil - see other questions, like this one.

Divine Providence

So your question isn't about evil spirits and how the relate to God necessarily, your question really is about how free moral agents can exist if God is in control of everything. As humans, angles, and evil spirits fall into that classification, the whole umbrella doctrinal category as it relates to this question is divine providence.

This is the central theological debate, between reformed thinkers, and Arminianist/Wesleyan thinkers, and somewhat more recently the Molinist thinkers. It may be difficult (or impossible!) to get a non-biased answer as a result as the debate still goes on, and any answer given would have to depend on the view of it's author.

However, you might check out this Wikipedia article on divine providence in Judaism for more info about how the original readers of that text may have interpreted it.

Similar to humans, the demons have their own freedom to act. God's control can be seen only as a limitation of devil's freedom, in sense that God will not allow to these spirits to affect the freedom of us as humans or other creatures. When Scripture says that "God sends an demon to do something ..." this must be always understood that "God lets/allows an evil to do that ..." because often the demons could provoke indirectly positive consequences, which can be foreseen only by God. Scripture states very clearly that "God will is always good", and "God is life".