Where are the angels who sinned? In hell or on earth?

The London Baptist Confession of 1644 notes the sin of the angels under article IV: ‘Satan…with his Angels having sinned before, and not kept their first estate, but left their own habitation…’  Nothing more is said regarding the sin of the angels because Scripture says nothing more.  God only indicates to us that the sin of the angels was to have departed from their original dwelling place.

2Peter 2:4  For if God spared not the angels that sinned, but cast them down to hell, and delivered them into chains of darkness, to be reserved unto judgment…
Jude 1:6  And the angels which kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgment of the great day.

Most recognise that 2Peter and Jude appear to be parallels of one another and give greater depth of the meaning intended by the Holy Spirit, in much the same way the four Gospels do.  Here, they are comparing the sinfulness and condemnation of the evil angels to that of false teachers and false brethren – ‘…to whom is reserved the blackness of darkness for ever.’ (Jude 1:13)
The  phrase used by Peter, ‘cast them down to hell’, is a single word, a verb – ‘tartarosas’.  Tartarus was the lowest place of Hades in Greek mythology. 

On 2Peter 2:4, with the angels being cast down into Tartarus, Matthew Poole writes:
‘What place that is we find not expressed in Scripture, and therefore we are not to be over curious in our inquiries after it’. 
I do not agree!  We must seek to know the will of God and we should be diligent in our studies.  If a matter is hard for us to understand, we must pray that the Lord would open our eyes.

What or where is Tartarus in the New Testament?

According to Strong’s Lexicon, this word is derived ‘[f]rom…Tartaros̄ (the deepest abyss of Hades); to incarcerate in eternal torment…’

Therefore, to tartarus someone, as this verb designs, is to cast them down in a spiritual sense; the ex-Pagan Gentiles would have readily understood the spiritual significance of this verb because the primary inhabitants of Tartarus, according to Greek mythology were the Titans - ancient deities who had been overthrown and cast down by Zeus and the Olympian gods.  Words and concepts were often used by the early Christians to convey ideas to their Pagan or ex-Pagan audience (eg. the Logos, Hades etc.).  But, as Peter and Jude tell us, this is not referring to that final judgment when the devil and his angels are plunged into the lake of fire; these chains of darkness are simply where they are reserved for that punishment – ‘not as equivalent to Gehenna, but as the place of detention until the judgment’, as Vincent’s Word Studies puts it.  And so this action refers to when the ‘sinning angels were cast out of heaven.’ (People’s New Testament commentary)

This understanding is further confirmed by the ancient Hebrew understanding of this verse in Peter's letter:

Aramaic Bible in Plain English - And if God did not spare the Angels who sinned, but cast them down in chains of darkness into the lowest depths and handed them over to be kept for the judgment...

Any confusion as to why Satan can roam around as a lion (1Peter 5:8) is therefore cleared up once we recognise that the evil angels are not in hell (Gehenna - the lake of fire).  So Jamieson-Fausset-Brown comments thus on Peter’s use of this Pagan Greek word: ‘ "Tartarus": nowhere else in New Testament or the Septuagint…though [the evil angels] final doom is hell, yet for a time they are permitted to roam beyond it in "the darkness of this world." Slaves of Tartarus…may also come upon earth.

So, how are the fallen angels incarcerated?  Simply put, God tartarus’ed, if you will, the evil angels in that He cast them down and they now inhabit darkness, particularly spiritual darkness and are in this jail, having received their prison sentence, now awaiting that punishment.   They left their original status and are now reserved in chains of darkness; they are kept in that outer darkness, no longer in the light of God’s presence.  Satan and his angels will not be cast into the lake of fire and properly tormented before the Day of Judgment (Matthew 8:29 & Matthew 25:41).

We see a symbolic vision in which the evil angels are cast down in the Revelation:

Revelation 12:9  And the great dragon was cast out, that old serpent, called the Devil, and Satan, which deceiveth the whole world: he was cast out into the earth, and his angels were cast out with him.

The casting down of Satan is also confirmed by the Lord Jesus:

Luke 10:18  And he said unto them, I beheld Satan as lightning fall from heaven.
And we see very clearly from the Scriptures that these evil angels do subsequently inhabit darkness. 

The evil angels inhabit darkness

In Psalm 78, the Holy Spirit describes the various plagues which God sent upon Egypt before the exodus of the Israelites.  The description of the plague of darkness is fascinating and very informative:

Psalm 78:49  He cast upon them the fierceness of his anger, wrath, and indignation, and trouble, by sending evil angels among them.

The Greek word used here for ‘evil’ in the Septuagint is used many times in the New Testament to refer to evil spirits (Luke 7:21, Acts 19:15 etc.) and so this cannot simply be referring to good angels who were sent to bring destruction.
Also, it is interesting, though by no means authoritative, to note how the Jews recalled the events of this darkness in which evil angels came to trouble the Egyptians.  We can see an account given in the apocryphal book of Wisdom:

Wisdom 17:2-4  When lawless people tried to oppress your holy nation, in actual fact they were the prisoners who were being held in a dark place, bound in chains through a long night. They were confined to their own homes as they vainly tried to flee from a plan that had been prepared for all eternity.
They thought that they could hide their sins by pulling a blanket of forgetfulness over themselves. But instead they were scattered in every direction, terrified by fear, and spooked by nightmarish visions.
They hid themselves in the deepest corners of their houses, but couldn't escape from their fears. Even there they heard all around them sounds that terrified them. Mournful ghosts with gloomy faces appeared to them.

Not only do the evil angels appear to have tormented the Egyptians by pretending to be ghosts but we also see that the darkness they experienced in this plague appears to be much the same as the darkness in which the Lord keeps the evil angels bound in chains, according to 2Peter and Jude.  Perhaps this is why Moses describes this darkness as a thick darkness which could be felt (Exodus 10:21-22).
But, more than this, we see why the children of God and of the devil are distinguished as being of the light or of darkness respectively:

1Thessalonians 5:5  Ye are all the children of light, and the children of the day: we are not of the night, nor of darkness.

Satan inhabits the darkness and the sinfulness which spiritual darkness seeks to conceal:

John 8:44  Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it.

But, Jesus Christ is the Truth itself; He is that God which is light, scattering the darkness and revealing all hidden things:

John 8:12  Then spake Jesus again unto them, saying, I am the light of the world: he that followeth me shall not walk in darkness, but shall have the light of life.

Jesus’ words in chapter 8 of John are significant; when we are told that Satan abode not in the truth, we have some idea then of how it is that the evil angels sinned to begin with.  To return to 2Peter and Jude, we see that the angels sin was that they ‘kept not their first estate, but left their own habitation’.  These angels didn't abide in the truth, the light –

Ephesians 5:13  …all things that are reproved are made manifest by the light: for whatsoever doth make manifest is light.

They departed from the presence of the Father of lights and abode in darkness.

Contentions

There are many who would and have contended that these angels must have been cast out into a bottomless pit, perhaps the one used symbolically in the Revelation (9:11).  But we can easily dismiss this notion with the following verses in which Christ encounters some men possessed with demons:

Matthew 8:29  And, behold, they cried out, saying, What have we to do with thee, Jesus, thou Son of God? art thou come hither to torment us before the time?
Luke 8:28  …I beseech thee, torment me not.
Luke 8:31  And they besought him that he would not command them to go out into the deep [the abyss].

From these verses we can gather that: the demons know they will be tormented at a certain time in the future, i.e. in the lake of fire; the demons also know that the Son of God will do this; they further equate this future torment with being cast into the abyss.  Therefore, as the demons understand their own punishment in the lake of fire and being cast into the abyss, we have no warrant to invent some other bottomless pit which either some or all of the evil angels now inhabit.  We might see symbolic beasts and locusts emerging from symbolic pits in the Revelation, but this is not explicit, like when Christ tells us of the fire prepared for the devil and his angels.  

The Greek word for ‘abyss’ is used in the Greek Septuagint version of the Old Testament to translate the Hebrew meaning of the deep places of the earth, particularly under the oceans (e.g. Genesis 7:11).  If the demons’ intent was to avoid going to this abyss, why dive into the sea once they had been cast out into the herd of pigs (Matthew 8:32)?
The abyss which the demons wish to avoid can be nothing other than their destined place of torment, the lake of fire, for this is where they shall be tormented:

Revelation 20:10, 13-15  And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.

…death and [hades] delivered up the dead which were in them: and they were judged every man according to their works.

And death and [hades] were cast into the lake of fire. This is the second death.

And whosoever was not found written in the book of life was cast into the lake of fire.

Conclusion

Again, we must conclude that both evil angels and wicked men will be cast into the lake of fire after the resurrection and the final judgment; and that the angels which sinned await their punishment whilst having been imprisoned in chains of darkness, roaming this earth.