In what language were the four Gospels and Paul's writings originally written?

Before I begin to give an answer, let me simply say that the question is not clear.

First, it pits the Greek manuscripts we have handed down to us against the testimony of the church fathers.

Second, it takes a stab into questions we have no definitive answer/evidence for: (e.g: "what language did Jesus speak?")

Third, it does not clearly distinguish between: (1) Original speaker (Jesus) --> (2) Language of first document (autograph) --> (3) Language of received text (Greek)

But since patristics is your interest, let's consider the church father, Eusebius as a case study. Concerning the gospels, here is his commentary in Greek:

“ Ταῦτα μὲν οὖν ἐν τῷ προειρημένῳ τίθησι συγγράμματι. Ἐν δὲ τῷ πρώτῳ τῶν εἰς τὸ κατὰ Ματθαῖον Εὐαγγέλιον, τὸν ἐκκλησιαστικὸν φυλάττων κανόνα, μόνα τέσσαρα εἰδέναι Εὐαγγέλια μαρτύρεται, ὧδέ πως γράφων· “Ὡς ἐν παραδόσει μαθὼν περὶ τῶν τεσσάρων Εὐαγγελίων, ἃ καὶ μόνα ἀναντίρρητά ἐστιν ἐν τῇ ὑπὸ τὸν οὐρανὸν Ἐκκλησίᾳ τοῦ Θεοῦ· ὅτι πρῶτον μὲν γέγραπται τὸ κατὰ τόν ποτε τελώνην, ὕστερον δὲ ἀπόστολον Ἰησοῦ Χριστοῦ Ματθαῖον, ἐκδεδωκότα αὐτὸ τοῖς ἀπὸ Ἰουδαϊσμοῦ πιστεύσασι, γράμμασιν Ἑβραϊκοῖς συντεταγμένον· δεύτερον δὲ τὸ κατὰ Μάρκον, ὡς Πέτρος ὑφηγήσατο αὐτῷ, ποιήσαντα. Ὃ καὶ υἱὸν ἐν τῇ καθολικῇ ἐπιστολῇ διὰ τούτων ὡμολόγησε φάσκων· “Ἀσπάζεται ὑμᾶς ἡ ἐν Βαβυλῶνι συνεκλεκτή, καὶ Μάρκος ὁ υἱός μου.” αὶ τρίτον τὸ κατὰ Λουκᾶν, τὸ ὑπὸ Παύλου ἐπαινούμενον Εὐαγγέλιον, τοῖς ἀπὸ τῶν ἐθνῶν πεποιηκότα· ἐπὶ πᾶσι τὸ κατὰ Ἰωάννην.” (6Euseb. 25:3-6 EUSEB-T)

Here is the provided English translation:

“ In his first book on Matthew’s Gospel, maintaining the Canon of the Church, he testifies that he knows only four Gospels, writing as follows: “Among the four Gospels, which are the only indisputable ones in the Church of God under heaven, I have learned by tradition that the first was written by Matthew, who was once a publican, but afterwards an apostle of Jesus Christ, and it was prepared for the converts from Judaism, and published in the Hebrew language. The second is by Mark, who composed it according to the instructions of Peter, who in his Catholic epistle acknowledges him as a son, saying, ‘The church that is at Babylon elected together with you, salutes you, and so does Marcus, my son.’ And the third by Luke, the Gospel commended by Paul, and composed for Gentile converts. Last of all that by John.”” (6Euseb. 25:3–6 EUSEB-E)

We notice a number of details:

First, his argument is from tradition. This is the difficulty of dealing with the fathers. Which tradition is reliable and which tradition is not? For example, Justin Martyr emphatically states that when Jesus was baptized the entire river was lit on fire (Justin, Dial. 88.3). Do we really expect that tradition to be true? So, when Eusebius states that the gospel handed down to us by Matthew was written in Hebrew, what evidence do we actually have for this?

The second challenge is an exegetical/linguistic one. What does "γράμμασιν Ἑβραϊκοῖς συντεταγμένον·" mean? In a formal translation approach, I'd translate it as "assembled together in Hebrew/Aramaic letters."' Especially that adjective, "Ἑβραϊκοῖς" is difficult, since it can mean both "Aramaic" and "Hebrew."

All of this shows us the difficulty in placing too high of an emphasis on the fathers. We have no way of determining the validity of what they write in matters like this. And, at a linguistic level, we have difficulty understanding what they wrote.

The other difficulty in this question is the many unproven assumptions it contains:

Now, Paul's Epistles must have been written in many languages. He wrote the Epistle to Romans so that scripture must have been written in Latin if it was for the Romans, plus Paul was a Roman citizen so he probably knew Latin. He has a lot of Epistles to Greek cities (Corinth, Thessalonica, etc.) which must have been written in Greek. Also, he has a letter to Jews so he probably wrote this in Hebrew.

Here's the challenge with addressing the thought brought up in this paragraph:

First, there is no evidence that Paul's letters were written in any other language than Greek.

Second, there is no evidence that Paul knew Latin.

Third, what is Paul's letter to the Hebrews? If you're referring to the book of "hebrews" as contained in our NT, then the conclusion scholars (not just atheistic ones) have reached based on the NT manuscripts we have is that we do not know who wrote the letter to the Hebrews.

Finally then, what languages and how many Jesus and his apostles knew and spoke becomes an interesting question. But it's a question we have no definitive answer to. What we have is the entire NT canon handed down to us in Koine Greek. That NT Greek then becomes our source and foundation. There are Latinisms in Mark's gospel. And there are many Hebraisms scattered throughout the NT. But the language the NT is written in Greek. So there is where we rest our attention and focus. Beyond that we move fairly quickly into idle speculation.

For most of the books of the New Testament, there is no tradition competing with the view that the book was originally written in Greek. I am aware of ancient tradition claiming a non-Greek origin for 3 of the New Testament texts: Matthew, Mark, and Hebrews.

Matthew

Every early Christian historian who wrote on the matter stated that the Gospel of Matthew was originally written in Hebrew, not Greek. Relevant testimony was given by Papias, Pantaneus, Irenaues, Origen, Epiphanius, Eusebius, Jerome, and others. This site offers a review of the statements made by early church fathers on the matter.

Those rejecting this view must claim that the early historians were unanimously wrong. This is a tall order considering that Pantaneus claimed to have a copy of Matthew in Hebrew, and Origen was one of the greatest Hebrew scholars in Christian history.

A textual witness to a Hebrew original may survive: Shem Tob Matthew. It's a copy of the Gospel of Matthew in Hebrew that was written into a 14th century Jewish polemic against Christianity.

George Howard, who published an extensive review of Shem Tob Matthew (The Hebrew Gospel of Matthew), contended that the Hebrew text was not a translation but was a corrupted descendant of an original Hebrew composition. One of the most compelling pieces of evidence he marshalled was the existence of numerous word-plays in the Hebrew text that are not present in Greek.

Since the author of the 14th century polemic was trying to discredit Christianity, it is implausible that he introduced literary flair into the text of Matthew--that would make the text look better; he wanted to make it look worse. If Judaism had in fact preserved a corrupted version of Hebrew Matthew for ~1300 years, it is unlikely other Jewish scribes would have added literary flourish to the text either.

My own work on the Synoptic Problem has led me to the conclusion that Matthew was originally composed in Hebrew, and the Greek is a translation.

The principal reasons many modern scholars reject the claim that Matthew was originally composed in Hebrew are:

• The belief that Hebrew was a dead language in the 1st century (The Dead Sea Scrolls discredited this claim; I review some of the evidence here: What Languages Did Jesus Speak?)
• The belief that Mark's Gospel was written first (I show that each of the major arguments for Markan Priority is circular, reversible, or both here: Deconstructing Markan Priority)
• The belief in naturalism (which, when applied to the New Testament, is question-begging)

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Mark

Although early historians are unanimous that Mark was composed in/near Rome, they do not specify whether it was composed in Greek (the lingua franca of the eastern empire and the early Christian church) or in Latin (the lingua franca of the western empire and of Roman government). There would be nothing unusual about a Christian missionary from outside of Rome teaching an audience in Rome in the Greek language: it's the one language both the missionary and everybody in the audience could be expected to understand.

The overwhelming majority of the evidence (manuscript, textual, patristic) supports the view that Mark was composed in Greek. Competing with this view are:

• The fact that Greek Mark has more Latinisms (Latin expressions ported into Greek) than all the other Gospels combined. This could be because it's a translation from Latin, but also could simply speak to the fact that it originated in a place where both Latin & Greek were widely used.
• A single manuscript, Miniscule 13, written in the 13th century, which directly claims that Mark was originally written in Latin.

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Hebrews

Most sources accept that the Epistle to the Hebrews was originally written in Greek. Competing with this view is the statement by 2nd/3rd century scholar Clement of Alexandria who stated:

the Epistle to the Hebrews is the work of Paul, and that it was written to the Hebrews in the Hebrew language; but that Luke translated it carefully and published it for the Greeks (as preserved in Eusebius Church History 6.14.2)

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Conclusion

The evidence for a non-Greek origin is strongest for Matthew. There is some evidence (later, less consistent) for a non-Greek origin of Mark and Hebrews. I am unware of any ancient witness supporting a non-Greek origin of any of the other 24 New Testament books.

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Re chronology, referenced in the OP, for a textual & chronological argument that the Gospels were written earlier (and for the Synoptics, much earlier) than 70-80 years after the crucifixion, see my video series here: Who, When, and Why - the Writing of the Gospels.