The Bible does speak of Nephilim after the Flood:

We have read about Nimrod, the man who rebelled against God and built a city with the tower of Babel.
He was a descendant of Cham, a son of Cush.But note the line of Canaan, another son of Cham. Genesis 10:15-20
Canaan turns out to be the progenitor of the many Nephilim nations: Deut 7:1-3 

From Deut 7, it is clear that God is striking these nations with a ban. Ban = Cherem (Hebr). They had to be completely destroyed in order to banish the Genes from the world. It is remarkable that the name Canaan is mentioned 157 times in the Bible and nothing is known about his life. God gives no attention to the Nephilim in the Bible!

After the tower of Babel, Canaan’s descendants occupy the land God intended for the bloodline of Seth. Satan here makes the next move in the ongoing battle for the Messiah. Satan, as a good observer, had seen that the promised land was important to God. And so he directed the progeny of the Nephilim to that land, the most important piece of land on earth.

So were there really Nephilim on earth after the flood?

Numbers 13:33….33 We also saw giants there, descendants of Enak, coming from the giants. We were like locusts in our own eyes, and so were we in their eyes. 

Amos 2:99 But I have swept away the Amorites before their eyes,
which were high as cedarand strong as oaks.
I have swept away its fruit from above and its roots from below
.

In Genesis 15:16 God says that the measure of the sins of the Amorites (giants) is not yet full…..9 But I have swept away the Amorites before their eyes,
which were high as cedars
and strong as oaks.
I have swept away its fruit from above
and its roots from below.

The Nephilim that Satan had sent to the Promised Land had to be exterminated by God: completely and utterly. God did this by using Israel as an instrument. And He helped them supernaturally.

When the Israelites, who were instructed to exterminate all the Canaanites, had accomplished this, it says in Joshua11:22 that they had all been exterminated except in Gaza, Gath and Ashdod.
22 None of the Enakites remained in the land of the Israelites. Only in Gaza, Gath and Ashdod remained.(And where did Goliath come from later?)Note: it was God who defeated the Nephilim by supernatural means. Remember Jericho, King Og and King Sihon (Numbers 21:21-26). ...21 Then Israel sent messengers to Sihon, the king of the Amorites, asking:
22 Let me pass through your land. We will not deviate through fields or vineyards. We will not drink the water from the wells. We will go by the royal road until we have passed through your territory.
23 However, Sihon did not allow Israel to pass through his territory, but Sihon gathered all his people and went out, meeting Israel, to the desert. Then he came to Jahza and did battle with Israel.
24 But Israel smote him with the sharp of the sword and took possession of his land, from the Arnon to the Jabbok, as far as the area of the Ammonites, for the area of the Ammonites had been fortified.
25 So Israel took all these cities, and Israel dwelt in all the cities of the Amorites, in Hesbon and in all the towns that were associated with it.
26 For Hesbon was the capital of Sihon, the king of the Amorites. He had fought the previous king of Moab and had taken all his land out of his hand, as far as the Arnon.

God gave these nations into their hands! The giant nations of Canaan (Genesis 15:18-21) heard this “hot news” and shivered with fear!
18 On that day the LORD made a covenant with Abram, saying, To your descendants I have given this land, from the river of Egypt down to the great river, the river Euphrates:
19 the Kenites, the Kenezites, the Kadmonites,
20 the Hittites, the Pherezites, the Refaites,
21 the Amorites, the Canaanites, the Girgasites, and the Jebusites.

Greek Mythology reflects the Nephilim:
The Greeks had many gods. At one point, the god Uranus (=heaven) has intercourse with the goddess Gaia (=earth) and their children are called Titans. Titans are like the Giants is another name for …. giants. After and battle with supreme god Zeus, the Titans are cast into the Tartarus. 

See below Wikipedia:

The Tartarus is the “hell” in Greek mythology. It is the unpleasant part of the underworld, and that is the great, sad realm beneath the earth, “as far removed from the earth as the earth is removed from heaven. In that realm of shadows, the god Hades, brother of the supreme god Zeus, wielded the scepter. With that, Hades was also the one in charge of the Tartaros, the worst part of the underworld. In the Tartaros, the spirits of those who had died, who had done exceptionally bad things in life or challenged the gods, were punished. Giants and monsters were also imprisoned there from time to time when they had incurred the wrath of the gods.

Is it possible that a 3rd invasion of fallen angels will take place?

That would have to happen in our time.
In Luke 17:26-30 Jesus says that the last days will be like the days of Noah and Lot. Jesus will not establish his kingdom unless first there will be a time like the days of Noah.
26 And as it happened in the days of Noah, so it will also be in the days of the Son of Man.
27 They ate, they drank, they took in marriage and they were given in marriage until the day when Noah entered the ark and the flood came and caused them all to perish.
28 In the same way also, as it happened in the days of Lot: they ate, they drank, they bought, they sold, they planted, they built.
29 On the day, however, when Lot left Sodom, it rained fire and brimstone from heaven and brought them all to perish.
30 So it will be on the day when the Son of Man will be revealed.

We live in such a time. Almost no one today expects God’s judgment on the world anymore, just as in Noah’s days. So when Jesus was asked about the end times he cites Noah and Lot.
Peter (2 Peter 2:4-7) and Jude (Jude 1:6-8) also cite Noah and Lot. Both begin by saying that the angels had sinned. The people of Jesus’ day knew the Book of Enoch very well and were familiar with its words.

2 Petr 2: 4 . … For if God did not spare the angels who sinned, but cast them into hell and gave them over to the chains of darkness to be kept until judgment;
5 and if God did not spare the old world, but kept the eight of Noah, the preacher of righteousness, when He brought the flood upon the world of the wicked;
6 and when God burned the cities of Sodom and Gomorrah to ashes and condemned them to destruction and made them an example for those who would live ungodly;
7 and when God redeemed righteous Lot, who suffered from the licentious lifestyle of normless people

Jude 1:6 And the angels who have not kept their original state, but have left their own dwelling place, he has placed in sure custody in darkness with everlasting fetters before the judgment of the great day.
7 Likewise it is with Sodom and Gomorrah, and the cities around them, which in the same way as they committed fornication and followed other flesh. They lie there as a warning example in that they are undergoing the punishment of eternal fire.
8 Nevertheless, even now these dreamers defile their bodies in the same way, and they reject authority and blaspheme all that is honorable.

Will the Hybrids reappear in our days?

Yes, it could be possible. We live in a time of genetic engineering and sexual sin. Both are widely accepted in today’s world. (See response to the Nashville statement)
Our generation is now prepared to no longer see these things as extraordinary!
In all media, books, TV, internet it is commonplace. There are even movies of parents with hybrid children.
Read Daniel 2: 40-43. Here you see a description of the future: the fourth and final kingdom.
40 And the fourth kingdom will be strong like iron, for iron crushes and pulverizes everything. Just as iron crushes everything, so this kingdom crushes and pulverizes everything.
41 That further you have seen the feet and the toes, made partly of clay from a potter and partly of iron – that will be a divided kingdom. It will have something of the hardness of iron – that is precisely why you saw iron mixed with muddy loam.
42 And the toes of the feet, partly of iron and partly of loam – that kingdom will be partly strong and partly brittle.
43 That you saw iron mixed with muddy loam – they will mingle by human seed, but they will not stick together, just as iron does not mingle with loam.

Notice verse 43: “they shall not mingle with human seed.”
People with Nephilim?
Possibly the mark of the Beast is a genetic factor. If you don’t have one, you will be excluded from everything, including economics!

What is certain is that today the spirits of the Nephilim, who are not yet chained in the “abyss,” are roaming around here on earth. They plague people and rebel against God.The spirits of the Nephilim are also called demons. (See Rev. 9)
1 And the fifth angel blew the trumpet, and I saw a star, fallen from heaven to the earth. And to him was given the key of the pit of the abyss.
2 And he opened the pit of the abyss, and smoke rose up from the pit like smoke from a great furnace. And the sun and the sky were darkened by the smoke of the pit.
3 And out of the smoke came locusts to the earth, and power was given to them, as the scorpions of the earth have power.
4 And it was said to them that they were not to harm the grass of the earth, or any green plant, or any tree, but only to those who did not have the seal of God on their foreheads.
5 And power was given to them, not to kill them, but to torment them, for five months. Their torment was like the torment of a scorpion when it stings a man.
6 And in those days men will seek death but will not find it. And they will long to die, but death will flee from them.
7 And the locusts looked like horses prepared for war. And on their heads they wore wreaths like those of gold, and their faces were like faces of men.8 And they had hair like the hair of women, and their teeth were like the teeth of lions.
9 And they had breast armor of iron, and the sound of their wings was like the sound of chariots with many horses rushing to battle.
10 And they had tails like scorpions, and there were stings on their tails. And they had power to harm people for five months.
11 And they had a king over them, the angel of the abyss. His name in Hebrew is Abaddon, and in Greek he has the name Apollyon.

Today, much scientific work is being done to improve the human race: we call this “Transhumanism.” For example, animals can obtain special characteristics through genetic manipulation of their genes. Examples are a hawk’s eye and a dog’s nose.All these developments and technical possibilities are moving towards the development of a “superhuman”. Already known is the development of the “super soldier”. Many of these scientific activities are done in the hidden and when it becomes known it goes under the banner of research into hereditary diseases and cancer.

Daniel describes the last kingdom, our time. Human seed will not mix with Hybrids. Possibly they are already among us! Many Christian and non-Christian sources confirm this.
The consequences will be disastrous. It will then be “as in the days of Noah”
(Matt 24:37).
36 But that day and hour is known to no one, not even to the angels in heaven, but only to My Father.
37 As the days of Noah were, so will be the coming of the Son of Man.