Is the God of the NT the same God as the God of the OT?

Yes. There have been many movements in the past within gnosticism such as marcionism that have tried to distance the two. Some church leader recently said we should be "unhinged" from the Old Testament which is totally wrong.

Reason some people cant seem to match the testaments together is the failure of churches to teach properly on the different covenants through which God operates. Many people make a mistake thinking there are two covenants in the Bible, old and new, this is not the case. Within the Old Testament books alone there are covenants made with Noah and Abraham prior to the covenant made with Moses and the people of Israel.

This is how all the differences are explained, God operates differently in the covenants He has made.

He is the same vengeful God today. All you see is judgement everywhere. But our role has changed to loving enemies and unconditional non violence.

Why has our role changed? I say its because of the covenant change

Regarding the question in the Title of the OP:

Yes

In your own understanding of history and mankind, have you ever paid close attention to whom it has been who has brought on the misery of mankind? From where I sit, I see it to be man, himself, never Go...Even the global weather has been brought on by man, however there is a certain halstorm that will come, but not before the very end, and that will truly be from our Father....Come back soon dear Jesus, Yeshua, amen.

How do you explain the huge difference of peace now and violence then between the covenants?

Well wrath is definitely a thing in both the new and old covenants. Wrath + vengeance = justice?

'Vengeance' isn't neccesarilly a bad thing for God...

Romans 12
12:19 Dearly beloved, avenge not yourselves, but [rather] give place unto wrath: for it is written, Vengeance [is] mine; I will repay, saith the Lord.
12:20 Therefore if thine enemy hunger, feed him; if he thirst, give him drink: for in so doing thou shalt heap coals of fire on his head.
12:21 Be not overcome of evil, but overcome evil with good.

I see no clear, obvious connection between your thread title and the content of your opening post, beyond the first two sentences.

Many times I have thought on "God's vengeance," and then my mind goes to the judgement of men, how their veryo own words will accuse them.
It seems to me the veangeance of our Father is doing nothing at all afdter people judge themselves. You must understand that people who do not love God do not want to have anything to do with Him, just as their masster, Satan.
Maybe I am wrong, maybe I am absolutely spot on, but I do not believe our Father needs that kind of satisfaction. I believe He alraedy has it.

So you think that God has changed? Do you see the OT God as vengeful? The OT God told His people He loved them and gave His blood for their salvation, do you think he lied about that? And what do you do with the line in the Lord's Prayer "hallowed be your name"?

Those scripture messages seems so clear to me but God speaks to the spirit not the flesh. I can't improve on God's word. Try prayer. Or perhaps they send a different message to you and you feel satisfied with what they tell you.

Why did he reduce some of them to cannibalism? Send famine and war. Like he does today?

But it was only on the 14th of Nisan in 30 AD that God brought the New Covenant into existence. Which means that while God is always the same, His covenants are not always the same. It is God who found fault with the Old Covenant, and therefore provided A BETTER COVENANT.

You still do not believe that Christ abolished the Old Covenant at the cross. You still do not believe 2 Corinthians chapter 3, or the book of Hebrews. You still do not believe that the Levitical priesthood was abolished and the order of Melchizedek (applicable only to Christ) was established.

SO ACTUALLY YOU DO NOT BELIEVE GOD. AND YOU OPPOSE HIS FINISHED WORK IN CHRIST.

That's rich, since all your posts tell us that you are wiser than God.

I think we have to recall that when tragedy occurs on a giant scale, like an earthquake that takes out a region of a foreign land, or as years ago when Katrina devastated parts of the United States, that there are people who will invoke God as the cause.

Perhaps we might realize that since God has told us He does not change and is the same as yesterday, today and forever, that the reason some may think today's God isn't the vengeful one we read of in the OT, is because people like those aforementioned one's aren't considered to be adding to the New Testament texts the actions of God, as they see it, and as was done in the Old Testament.

God sent the global flood. (The Book of Genesis chapter 6)
God destroyed Sodom and Gomorrah, (Genesis 18) out of vengeance for the sins committed there. Just two examples that tell us, while the new covenant reconciles us to God, God is still the same Holy Spirit "he" was in the old covenant. Only now when those aforementioned types state that the devastation that occurred on a mass scale was God's vengeance for whatever sin they name, those people are often mocked, even by Christians, and are dismissed as kooks. Even by television pastors of the fundamentalist type.
That's what can lead to people thinking there are two different God's referred to in the two covenants. When Christians say, no it isn't possible that Katrina was God's wrath for these sins.... It leads people to ask the question: then why was God the one responsible for the devastation of the first born of every Egyptian house? (The Book of Exodus chapter 11)

Some Christians will deny all that. While others will defend God saying, He's God. He can do whatever He likes with his creation. And those to positions in and of themselves put Christians at odds with the question asked early on in a different thread. "Is God a moral monster?"
If we did as God did to our enemies, would we be considered to be in Christ?

I know, "It's a mystery."
No, it's in the Bible.
God loves us.

I'm not looking for understanding on the nature of God, but rather on the connection between your title and the content of your post.

It gets old reading the undisciplined unfettered personal assaults that regurgitate themselves in these forums.

Our precious Father tells us to pray for our enemies. I did not see any scripture that tells us we must concede to that enemy action so as to remain a target under their feet, nor of and to their hate filled tongues. Imagine how starve an enemy becomes if you simply pray them attention, rather than pay them attention.
Continue to live the peace of Christ. It really makes them angry. As you can see. And nothing you say or do will stop the advance of the evil aligned against you sister. They are legion.