Jesus was speaking of demons coming in an occupying a person's physical body.
The "house" in the parable refers to the physical body.
The "strong man" is the living being - the spirit-person who is occupying that physical body.
Each of us is a spirit-person, and each of us are temporarily occupying our physical body much as a driver is occupying and driving an automobile. Jesus is describing this spirit-person as a "strong man" because in a healthy situation, the inner person - the spirit-person - has a firm grasp of the physical body due to our identification with it.
The "anyone" in Jesus' parable is referring to any ghost - demon - who would attempt to come in an occupy the person's physical body.
Before such a ghost spirit-person could come in and occupy the physical body, the spirit-person who is already occupying the body (the "strong man") would have to be tied up.
Thus Jesus is describing the mechanism by which a demon-ghost may possess a person's body.
So how can the spirit-person who is occupying the physical body be tied up? This can take place under several scenarios. One of the easiest is during intoxication. During intoxication, the spirit-person's neurological grasp of the physical body is weakened. This is illustrated by the loss of balance, perception and other physical signs of intoxication.
Possession can also take place during illness, severe depression, anxiety and other mental states whereby the spirit-person within seeks to withdraw from the physical body. Typically this will also accompany drugs as well - which again produces intoxication.
So what does "carry off his possessions" mean?
When a demon-ghost forces into a physical body and possesses it, they are in fact "carrying off" - or taking control over - the former possession of the spirit-person who occupied the physical body previously. The body was the possession of the spirit-person, and now it is in another's possession.
This is why they call it demon possession. Someone else is possessing the body rather than the spirit-person who was assigned to that physical body.
As discussed previously, the facility for removing such a ghost-demon from a possession requires the participation of the Supreme Being and His representative. God's Holy Names can both prevent and facilitate the removal of a ghost-demon, but these are best utilized with an invocation of the Supreme Being's representative - which doubly serve to repel the demon.
The reason being, demons don't like God's Holy Names, and they don't like to deal with those who are serving the Supreme Being. They are repulsed by the Supreme Being because they see themselves as supreme. They see themselves as the greatest and they don't want to praise the Supreme Being or deal with someone who is loving and serving the Supreme Being, as Jesus is.
(For a translation of Jesus' statements from the Book of Matthew without institutional sectarian influence, see the Gospels of Jesus - translated from the original Greek texts.)