The Bible says that we may be entertaining angels unawares.  What about demons and demon possession?

There are several differences between angelic interaction with man and demonic interaction with man.  Angels interacted with men in Old Testament times (cf. Gen. 18-19), but there is no record of demon possession in the Old Testament.  The New Testament implies that angels continue to interact with man, albeit in an unknown way (Matt. 18:10; Heb. 1:14; 13:2), whereas both Testaments show that demonic possession was only a temporary phenomenon (Zech. 13:1-2; Heb. 2:14-15; 1 John 3:8).

To elaborate, Christ was sent to save the lost (Lk. 19:10) “in the fullness of time” (Gal. 4:4), i.e., at the right time.  To save us, He had to destroy both the devil (Heb. 2:14-15) and his works (1 John 3:8)…all his works.  Thus, God allowed demon possession during this time to show Christ’s complete authority over Satan in all realms, including the spiritual (cf. Lk. 4:35-37; Matt. 12:22-29).  The purpose of miraculous demonic expellation (Mk. 16:17) was to confirm the Word of God that was being preached (Mk. 16:20).  Once the Word was completed, miracles would cease (1 Cor. 13:8-10; cf. Rom. 12:2; James 1:25).  That took place 2,000 years ago.  Thus, demonic possession stopped at the same time, as was prophesied in the Old Testament (Zech. 13:1-2).