According to Catholicism and/or Eastern Othodox, if we have Guardian Angels do we also have an assigned Demons? The idea of having a demon assigned to us isn’t new to anyone who is familiar with C.S. Lewis and the Screwtape letters.  Since the idea (according to Catholic and Orthodox Tradition) is that God “assigns” us each a Guardian Angel is it likely we also have a demon assigned to us?  

I can’t comprehend how the world of angels and demons exists but if there is an eternal struggle for our souls it would make sense.  

From a biblical perspective Acts 12:15 New International Version (NIV)
15 “You’re out of your mind,” they told her. When she kept insisting that it was so, they said, “It must be his angel.” - Seems to support the notion of guardian angels.  

King James Bible  Matthew 18:10
Take heed that ye despise not one of these little ones; for I say unto you, That in heaven their angels do always behold the face of my Father which is in heaven - Is another example.  

Through my research the term guardian angel or guardian demon is not found within scriptures.
Jesus says of the little ones who make up the kingdom of heaven :


  Take heed that ye despise not one of these little ones; for I say unto you, That in heaven their angels do always behold the face of my Father which is in heaven. Matthew 18:10 KJV.


So, yes, I also believe that the children of the Father, born from above, redeemed by Christ, have angels (one at least) "assigned" to them.

From the incident regarding Peter, quoted in the question, it seems clear to me that the angel which assisted Peter to escape from prison had probably helped him previously and this was known among the church, therefore they said (on this occasion), 'It is his angel' because they were already acquainted with the angel's existence and guardianship.

The redeemed, previously, were indwelt by unclean spirits, demons, as we see in many places in the gospel accounts. Out of one man, the Gadarene, there went a whole legion of demons, enough to cause a whole herd of swine to rush off a precipice into the sea, Matthew 8, Mark 5, Luke 8.

Out of Mary of Magdalene, there went seven demons, and she was delivered of them.


  And certain women, which had been healed of evil spirits and infirmities, Mary called Magdalene, out of whom went seven devils, Luke 8:2 KJV.


Jesus warns us that, being once delivered, and the house (of our soul) being 'swept and garnished' we should not have the place just . . .  vacant.


  When the unclean spirit is gone out of a man, he walketh through dry places, seeking rest, and findeth none. Then he saith, I will return into my house from whence I came out; and when he is come, he findeth it empty, swept, and garnished. Then goeth he, and taketh with himself seven other spirits more wicked than himself, and they enter in and dwell there: and the last state of that man is worse than the first. Matthew 12:44 KJV, also Luke 11:25.


Those who believe the gospel and follow Jesus Christ are to be full of the Holy Spirit and are advised, by the apostle Paul :


  That ye put off concerning the former conversation the old man, which is corrupt according to the deceitful lusts; And be renewed in the spirit of your mind; And that ye put on the new man, which after God is created in righteousness and true holiness. Ephesians 4:22 - 24 KJV.