Some people neglect the subject; others over-emphasize it. Angels are mentioned about 300 times in the Bible, plus demons, and devils. The Seraphim and Cherubim are not angels.
Nature: They are spirits (bodiless), though they take on human form in order to appear to people. They do not have wings. They are sexless, and do not reproduce (this makes men superior). They seemingly were created simultaneously, and before man was (Job 38:7). They are called “sons of God” but are likely not (Gen 6:2). While equal, they are not identical, but vary and have internal organization (cf. 2 who are named). They are “numberless”. Since the fall of some, faithful ones seem fixed in holiness. They are not omnipresent, but ubiquitous; not omniscient, but very wise; not omnipotent, but extremely powerful (II Kings 19:35). Their influence is not just physical, but mental, and spiritual. Especially good ones upon evil (Rev 12:7). The Second Person of Trinity appears in the Old Testament as “the angel of the Lord”.
Purpose (Usefulness): It is not to “glorify God” in “Old King Cole” fashion, but by serving us! (Hebs 1:14) Problem: Why does God use such instruments, when He could do the same directly, without means? One answer is to demonstrate His infinity by creation of this unique type of creature. Also, the fall of some who set up a competitive kingdom, fitted into His redemptive program. (No gold without fire; no diamonds without pressure; no muscle without exercise.) The word “angel” means messenger (in Rev. 2,3 it may refer to a human). They likely communicate much good to us, just as Satan puts bad thoughts in our minds. Matthew 18:10 and Psalm 91:11 suggest “guardian” angels. Their protection from spiritual harm will likely amaze us in Glory. The communication of the Law via angels (Acts 7:53, Eph 3:10, Hebs 2:2) is intriguing. Jesus was ministered to by angels after Temptation and in Gethsemane.
Relation to Men: Hebrews 1 & 2 speak much of this, quoting Psalm 8. Originally they were “inferior” (see above), but not because man was created in “knowledge, righteousness, and holiness”; the angels excelled innocent man on this count. At the Fall, man became inferior ethically, and subject to Satan, a fallen angel. In Christ we are restored again to command of the angels, good and bad. Our righteousness is superior, and our new nature is too.
Evil Angels: We do not know when the fall of Satan and his followers took place. (It would seem that man’s probation was not an extended length of time.) Rev 12:4 suggests a large number, though a minority, became evil. (It should be remembered that they kept all their angelic gifts, only now used to evil purposes – though, as in the case of the good ones, only as God allows.) The “cause” of the angel fall is uncertain. It was presumably pride, independence (which is basic to all human sin too.) Isa 14:12 can serve as a “picture” of Satan’s fall, but it actually is describing the kingdom of Babylon (vs 4), who was a tool of Satan.
Demon-Possession (and exorcism): We all are influenced by Satan in degrees (Matt 16:23). Possession seems to be a matter of “complete” control. It can be multiple (Mk 9:5). It can display various symptoms; physical ailments, mental, moral (Lk 22:3). It occurred much in the time of Christ. If today, it would seem in heathendom, especially when the Gospel makes its first inroads. The “binding of Satan” (Rev 20) seems limited to control of dominant nations. (Began at Ascension of Christ? Rev 12, Mt 12:29, Lk 10:18)
Exorcism is not done via formulae, even holy ones (Acts 19:14); ritual is Satan’s speciality! It is not permanent (Mt 12:45); the recipient should be receptive (Jesus often asked beneficiaries of physical cures if they wanted them); it is significant that exorcism is not listed in the gifts of the Spirit or offices of the Church. Unbelievers perhaps can exorcise, to convulse people. The ideal “immunity” is to be filled with the Spirit. Paul mentions prayer repeatedly in his discourse on resistance against Satan in Ephesians 6.
One important point regarding Satan which many Christians do not realize is that ALL evil (sickness, bad weather, war, ca.amities) is from Satan. God uses these for believers’ good, but does not “cause” them. (Job, Lk 13:16, I Thes 2:18, II Cor.)