Unlike the burning of Mount Hiei and Enryaku-ji which seem to have been blown all out of proportion by legend, the burning of Nakae and Yanagashima is most likely true. Interestingly two contemporary chronicles do not mention the specific incident, one saying that two months of fighting resulted in 20~30,000 casualties on both sides, including four of Nobunaga's brothers and seventeen other ranking samurai, with Nobunaga displaying the heads of there enemy leaders at Nijō street in Kyōto. The other, the chronicle of Tōji temple in Kyōto, says over the two months, the Ikkō, the Oda forces, and "other temple and lay men and women totaling few ten thousands the exact numbers unknown" were killed or drowned at sea. Early Edo records do not seem to mention the incident either, instead focusing on its cause (Mid-Edo records have both, likely using earlier records). But as we have two fairly contemporary and fairly reliable histories both saying similar things, these other sources while not mentioning the incident explicitly seem to support the two histories and the event's historicity. At the very least four separate contemporary records all mention the extremely high death toll, so whether it was mostly in one day or the total over two months, the campaign was extremely bloody.
So a bit of a background. In 1570 when Ōsaka (Ishiyama) Honganji decided to actively resist Nobunaga and called on Ikkō supporters throughout Japan to do the same, the Ikkō of Ise assaulted Nagashima and the surrounding castles located in the Kiso and Nagara river delta. One of Nobunaga's younger brothers, unable to hold his castle, committed suicide when it fell. After repeated attempts against Nagashima, in 1574 with the alliance against him completely broken, Nobunaga gathered a huge force and marched on the river delta from multiple directions from both land and sea.
According to Jesuit Luis Frois' History of Japan, one day, the Ikkō forces ambushed the Oda forces, killing a thousand men including two of Nobunaga's half brothers, one cousin, and one nephew. A few days later Nobunaga attacked from land and sea with everything he got, killed 20,000 people in a day, took the castles in the area, and sent the heads of the highest ranking monks to the capital.
One of the Oda retainers, Ōta Gyūichi, wrote the Chronicle of Lord Nobunaga and it offer some more details. In summary, fighting began in early August, and through burning, assault, and naval bombardment (one of the earliest in Japan), the Ikkō forces were driven back into Nagashima, Yanagashima, Nakae, Shinobase, and Ōtorii Castles. When Shinobase and Ōtorii were surrounded and their defenses were broken up by bombardment and just before the assault, the castle defenders begged for pardon. But instead, Nobunaga answered that he'll starve them to death as example to others and for all their insolence and ravaging over the years. He might also have wanted revenge for his brother, but that's just my "conjecture". I jest, but sources like the early Edo Tōdaiki explicitly say Nobunaga had a grudge against Nagashima for his brother's death in 1570, so it's pretty widely acknowledged. Anyways under cover of darkness and rain, the Ōtorii defenders tried to make a break for it, but were caught and a thousand men and women were killed. The Shinobase defenders told Nobunaga they'll convince Nagashima to surrender, so they were driven into Nagashima, but the castle did not surrender and so we reach the end of August.
By mid October half of the defenders of Nagashima, Yanagashima, and Nakae had starved to death. The defenders of Nagashima sent word that they'll surrender the castle, and tried to leave by boats. However, Oda forces shot and attacked the evacuating defenders. A group of them at that moment stripped naked, drew swords, and charged the Oda ranks, killing 700~800, broke through, killed many of the Oda family (according to the Oda Clan family tree this included Nobunaga's older brother and one younger brother) before escaping into the nearby mountains. The Oda forces responded by building barricades around Nakae and Yanagashima castles, trapping about 20,000 people, and then setting the castles on fire.
So Nobunaga might have killed 20,000 people in a day. Or that might have been the total over about two months of fighting, with a lot of them having starved to death rather than burnt alive. According to the Chronicle, Nobunaga seem to have already decided to kill them all early in the campaign, though by starvation. Either way, Nobunaga's revenge for killing his family extracted a much higher body count than a lot of his most famous battles.
Where can I read more about these so-called set piece atrocities? legend or otherwise.