These are the attacks he uses with two swords. Nitoryu was also Zoro's original fighting style when he began to learn how to wield a sword, before accepting Kuina's sword and practicing Santoryu.
Before the Timeskip
Taka Nami (鷹波,Taka Nami?, literally meaning "Hawk Wave"): While airborne, creates a powerful gust of wind to knock opponents over. It was first used to wipe out some Baroque Works agents at Whisky Peak. It can be done while standing on the ground. Zoro says this attack is very useful against a group of weak enemies. The pun here is Takanami can mean "high waves" in Japanese. This attack was the first non-Santoryu technique Zoro uses in the series. This is called Hawk Wave in the VIZ manga and FUNimation dub.
Sai Kuru (犀回,Sai Kuru?, literally meaning "Rhino Revolve"): Zoro holds his swords in front of him pointing up, like rhinoceros horns, and spin-slashes around himself in an instant (almost akin to Tatsu Maki, but more briefly). This was first seen being used against the Franky Family when they "ambushed" Zoro on the Going Merry. Pun with the Japanese pronunciation of the English word "cycle". This is called Rhino Cycle in the VIZ manga and FUNimation dub and Rhino Rampage in the English version of One Piece: Grand Battle! Rush! (dubbed by 4Kids).
Nitoryu Iai: Rashomon (二刀流 ｢居合｣ 羅生門,Nitōryū Iai: Rashōmon?, literally meaning "Two Sword/Blade Style Re-sheath: Thin Life Gate"): A dual sword drawing technique so powerful that it can split large obstacles in half. Zoro draws his swords, and sheathes them quickly, able to split two train carriages in half. Built in the year 789, the Rashomon was arguably the grandest and most famous gate in Kyoto. The name of this move probably comes from the double-gate/double-sword connotation, as well as being the 'grandest move' in his Nitoryu lineup. This was first seen being used to cut open two sea train carriages filled with Marines and World Government agents (none of the passengers were harmed at all). In the VIZ manga, this is called Two-Sword Style Castle Gate. In the FUNimation dub this is called Two-Sword Style Sword Draw Rashomon. In the english localization of One Piece: Pirate Warriors 3, it is called Castle Gate. It is also used as a counter/reversal in Jump Ultimate Stars as opposed to a direct attack.
Nanajuni Pound Ho (七十二煩悩鳳,Nanajūni Pondo Hō?, kanji meaning "Seventy-Two Klesha Phoenix"; furigana meaning "72 Pound Phoenix/Cannon"): Same principle as the 36 Pound Cannon. Holding his two swords horizontally above the shoulder, Zoro then performs a circular swing that launches two air compressed projectiles spiraling towards the target instead of one, making it twice as powerful. This was first seen being used against Kaku to counter his "Rankyaku: Hakurai" technique.This is called 72 Pound Phoenix in the VIZ manga, and 72 Caliber Phoenix in the FUNimation dub. The attack's name is actually a very heavy pun, it is written out as "Phoenix of the 72 Kleshas" in the manga with a skewed reading attached that makes it "72 Pound Ho" when read out:
Ho means both "cannon" and "phoenix"; however, the attached kanji is for "phoenix", making that the literal translation and the "cannon" reading a pun on that, both of which are correct.
The "pound" part is a skewed reading of the kanji bonnou for "klesha", a Buddhist term for "worldy desires of evil thoughts", and it is referring to the Caliber of a Cannon (a 72 Caliber Cannon would fire a 72 Pound Ball).
In Pirate Warriors 3, when used as the second input of his inverted C3 chain (Trianglex2, Squarex2), Zoro instead runs with both swords at his left side for a rushing double-swing to his right, though no projectiles emerge whatsoever (and the final input leads into his 1080 Pound Phoenix).
Nigiri (弐斬り,Nigiri?, literally meaning "Two Cutter"): A stance where two swords are held parallel so that the tips are pointing to his right or left side, this move is like a pre-requirement to perform: Toro, Otoro, Hirameki, Samon, and Maguma. The pun in this is taken from sushi - the "Nigiri" in "Nigirizushi" roughly means 'hand-rolled'. This was first seen being used against Kaku. In the FUNimation dub this technique keeps its original name.
Toro (登楼,Tōrō?, literally meaning "Climbing Tower"): Two air-based projectile slashes are sent upwards while jumping as Zoro swings his swords in an upward motion. The pun in this is that "Toro" is an expensive cut of tuna for sushi; a more fatty cut than the normal, while the technique's kanji is an actual term for climbing a tower (or to "visit a brothel"); another difference between the tuna "toro" has no extended vowels, while the tower-term "tourou" has two extended "u" vowels when written in romaji. This was first seen being used against Kaku. In the VIZ manga and FUNimation dub, this is called Tower Climb.
Otoro (応登楼,Ōtōrō?, literally meaning "Reply Climbing Tower"): Two air-based projectile slashes are sent downwards while falling as Zoro swings his swords downwards, with the gravity complimenting the force of the attack. The pun in this is that "Ootoro" is an even more expensive cut of tuna for sushi; the underbelly which is said to be the most flavorful flesh (though in romaji, the kanji for "reply" has another extended "u" vowel as "ou" instead of an "o", making it "outourou"). This was first seen being used against Kaku. In the VIZ manga and FUNimation dub, this is called Tower Climb Return.
Hirameki (閃,Hirameki?, literally meaning "Flash"): Two air-based projectiles are sent forward after swinging both swords from the left or right side. The pun in this is that "Hirameki" is a type of sushi buffet, while "hirameki" is also the kanji's kun'yomi reading. This was first seen being used against Kaku. In the VIZ manga and FUNimation dub, this is called Flash.
Samon (砂紋,Samon?, literally meaning "Sand Drawing"): Two air-based projectiles are sent diagonally down and to the left or right after swinging both swords from the left or right. The pun in this is obvious; it sounds like "Salmon", a common fish used for sushi. This was first seen being used against Kaku. In the VIZ manga and FUNimation dub, this is called Ripple.
Maguma (魔熊,Maguma?, literally meaning "Demon Bear"): A simple downward pound into the opponent with both swords. This was first seen being used against Ryuma. The name may be a pun on the Japanese pronunciation of "Magma". In the VIZ manga and FUNimation dub, this is called Demon Bear.
Dai Gekken (大撃剣,Dai Gekken?, literally meaning "Great Fencing Sword"): Zoro pierces two of his swords into Franky's heavy nunchaku and hits the opponent with it. This was first seen being used against Oars. In the VIZ manga and FUNimation dub, this is called Great Shock Slash. "Gekken" literally means "Striking/Attack Sword", which is normally a Japanese term associated with fencing.
After the Timeskip
Nigiri: Toro Samon (弐斬り 登楼砂紋,Nigiri: Tōrō Samon?, literally meaning "Two Cutter: Climbing Tower Sand Drawing"): A combination of two former techniques, Toro and Samon, performed from his Nigiri stance. Zoro uses two swords in an upward diagonal slash to send a double air-based projectile attack that cuts his opponent. The pun is that Nigiri is a type of sushi, Toro means fatty, and Samon is a homophone for Salmon in Japanese. Put it together and it is Fatty Salmon Sushi. It is called Nigiri Tower Climb Ripple in the Funimation subs. This was first seen being used against Basil Hawkins.
Nanahyakuniju Pound Ho (七百二十煩悩鳳,Nanahyakunijū Pondo Hō?, kanji meaning "Seven-Hundred Twenty Klesha Phoenix"; furigana meaning "720 Pound Phoenix/Cannon"): A more powerful version of the 72 Pound Cannon. Holding his two swords horizontally above the shoulder, Zoro then performs a circular swing that launches two air compressed projectiles spiraling towards the target. The attack was first seen being used against Kurozumi Orochi, though it was deflected by Kyoshiro.
Despite being the style Zoro is most used to (he began using three swords right after Kuina's death and he once said he was not very good with one sword), his Nitoryu techniques are the only ones that have not been used as a finishing move against a powerful named opponent.
Nigiri Is a type of sushi and Zoro's attacks in Nigiri are mostly sushi puns.
Zoro's Nitoryu is based on the Niten Ichiryu (Two Heavens-as-One Style), one of the first styles of samurai swordsmanship that focus on dual-wielding swords in battle (famously used by the famed samurai and the Sword Saint, Miyamoto Musashi).
While not officially called a Nitoryu technique, Zoro's uses two swords when using Homura Saki.