Only people can be demonically possessed. But inanimate objects can be negatively controlled through curses. As Adam Blai, a lay Catholic expert on religious demonology and exorcism, writes:
A curse is simply a demon sent to do some harm. . . . Cursed objects are objects that have had the opposite of a blessing done to them. Instead of grace being attached to an object to make it holy, a demon has been attached to the object to make it associated with evil (Hauntings, Possessions and Exorcisms, p. 45).
That is, through the permission of the one who has rights over an object, a demon attaches itself to the object and inflicts harm through it.
We can also distinguish between the cursing of an object and an object’s being impacted via demonic infestation. Infestation refers to when demons have obtained the right to carry out extraordinary manifestations in specific locations, such as a house, an example of which could be the moving of a non-cursed item(s) into the house.
In addition, in an attempt to intimidate exorcists and others involved in spiritual warfare, the devil and his demonic minions may perform extraordinary manifestations apart from curses or infestations that could include physical attacks the type of which St. Padre Pio, for example, endured. For more on this general topic, see the website of Adam Blai.
I’m not aware of any case of a cursed object in the Bible, but Jesus did allow the demonic group called “Legion” to enter into a herd of swine after exorcising them from a man (Mark 5:1-20).
As for dreamcatchers, they hypothetically could become cursed or impacted otherwise by a demon. But we should not become preoccupied with such matters and instead trust in our Lord and his Church.