This might be a better question for /r/linguistics

More of course can be said here, but /u/limetom reponded to a similar question recently which I think will be of interest for you!

In short terms not really.

Classic Japanese is quite different to modern Japanese with many grammatical differences as well as a large difference in vocabulary used. This change gets much larger the further back you get. So if you have a Heian period text like Genji Monogatari then it has a lot more differences than for example a Meiji Period text like, say Gakumon no Susume.

Getting into the details of it is hard to explain without assuming a high level of knowledge of Japanese language, but basically in the 19th and 20th century Japanese language was effectively “simplified” by the government, leading to large changes. For example, in old Japanese texts a word would take a specific grammatical form known as the rentaikei (連体形) in the case it modified a noun, but this was removed and barely exists now in modern Japanese. Lots of other similar changes were made which means that in particular in terms of grammar there are a number of differences between modern and Classical Japanese m, but also in terms of vocabulary as well.

If we put it in terms of your original question, no a current Japanese person couldn’t really have a full conversation with Oda Nobunaga. Someone earlier and even less of a chance, but more recent such as Meiji era and perhaps so. All Japanese students study Classical Japanese at school as a requirement and are made to make modern translations of old texts, however, translating an old text and actually being able to speak it are two different things. Indeed, our current understanding of Classical Japanese is based on what we THINK that things were pronounced as. Words when written down end in syllables that they wouldn’t end in now, and syllables that are now combined and pronounced at one are written down separately. When translating we assume that these are pronounced the same way we pronounce them now, but as we have no voice recordings from the time we have no way of knowing how they were actually pronounced.

If I sort of wrap it up together, no, a modern japanese person could not have a conversation with Oda Nobunaga efficiently. While Japanese students do study Classical Japanese at school they have no training in actually speaking the language, and as a result the vast majority would not be able to efficiently construct appropriate sentences. In particular as we go further back to the 1600s and before that these differences get more pronounced. To add on top of that we actually have no way of knowing for sure that Classical Japanese was even pronounced the way we think it was, and adding all these elements together it’s very very unlikely the average Japanese adult would be able to hold a detailed conversation with a character from several hundred years ago

I'm not an expert, but have studied both modern and classical Japanese and a fair amount of Japanese history, so I'll do my best to answer.

The first thing to understand with historical Japanese is that there is a clear distinction between the written and spoken language. During the Heian era (794-1185), when Japanese literary culture was at its peak, the rules of bungo (文語) or 'literary language' were codified. Bungo is almost entirely different from modern Japanese. I would try to explain how it works, but it's just too complex to really get into here. If there's interest, I'd be glad to explain it in a follow-up comment.

The rules of bungo as codified in the Heian era remained essentially static for the next 1000 years. Virtually ALL written documents in Japan from the 9th-19th century were written in bungo following the grammatical guidelines set out in the Heian. Official legal documents even remained written in the language until after WWII. It is also still taught today as a mandatory part of the Japanese high school curriculum and so is still alive and well, though the more common name for it these days is kobun (古文), literally 'old writing'.

While bungo remained mostly static for about a millennium, spoken dialects of Japanese followed a very different path and would have varied significantly depending on geographical location and social status. Unfortunately, it is very difficult to verify how people spoke prior to the Edo period (1600-1868) as virtually all written documents prior to this have been lost in the many wars Japan has fought. In addition, the fact that bungo was the official language for all written documents throughout this time means that very few documents were written in the vernacular to begin with. Someone who knows more about historical Japanese vernaculars can probably shed more light on the topic.

To answer your question about whether or not a modern speaker would be able to converse with Oda Nobunaga, I'd say it's fairly unlikely. Since he was a nobleman, his family would likely have spoken a complex form of the language with lots of honorifics and a grammatical structure similar to bungo. Plenty of elements of this language have made its way into modern Japanese, but these are mostly token phrases that don't fit the grammatical scheme of the modern language.

Hopefully that's a satisfying enough answer. I've only got my BA in this stuff but am preparing to enter grad studies soon, so my understanding is fairly basic and I could be wrong on a number of points.

I think, because Japan has this image of itself as culturally homogenous and unchanged for thousands of years through to the future, it's also really important to note how diverse the language was up until the modern period (when it was quite forcefully made to seem less diverse to outsiders). There was no such thing as "standard" spoken Japanese during the medieval period or the early modern period, though there were certainly more "influential" dialects than others (and, due to his position, Oda Nobunaga would certainly be able to understand those), depending on where the capital was located; in the medieval period it was the Kamigata dialect (related to modern-day Kansai-ben) and during the Edo period it was Tokyo-ben. However, it's important to note that there was significant variation in dialects in the various regions of the country, and even contemporaries had trouble understanding "common people" from different regions.

When Koshouken Furukawa (from the then Bitchu province, present day Okayama prefecture) accompanied shogunate inspectors on an inspection tour of Touhoku and Hokkaido in 1783, he noted these differences in his travelogue. When he was visiting the Aizu region (modern Fukushima) he notes that "both sides can understand only half of the other's language." And in Nanbu domain (modern Iwate prefecture) he says: "The language of both men and women was gibberish, with only two or three words out of ten being comprehensible. The local lords usually give each inspector, in addition to his guides, two or three people well-informed about the castle town for the duration of his stay. The lord of Morioka Castle gave us two interpreters in addition because the speech of this part of the Nanbu domain is notoriously incomprehensible. But even the interpretors often could not understand what people say here."

Even during the Meiji period, Hideo Horie noted in his "Treatises for the Reform of the National script in 1902 that "more than saying that people from Kyushu and Touhoku simply could not understand each other, it would be better to say that things were in a complete state of chaos" and warned that "the unification of the National Language is an urgent task for our subordinates." It was really from this period (the Meiji) on that there was a really conscious effort to create a "standard" Japanese that everyone in the country could speak and understand, and in the process many dialects were left for dead, though certainly many still survive (though their speakers would know how to speak the national dialect as well).

I know you asked whether someone today could understand an elite person (Oda Nobunaga) in a conversation, but I thought it would be worthwhile to point out that, though it would be difficult to understand Nobunaga, it would be 10x more difficult to understand a common person from Fukushima in the early modern period. That is to say that there was really never such a thing as a standard "Japanese" language.