Law is a fearsome pirate who, along with most of his crew, proved resistant to Rayleigh's burst of Haoshoku Haki that took out almost everyone in the Auction House. Even Donquixote Doflamingo commented to his subordinates at Punk Hazard about Law's potential, comparing it to Luffy's, which Doflamingo witnessed himself during the war at Marineford two years ago; Doflamingo saw talent in Law, and intended to make him into his right hand man, as well as reserved the Heart seat for Law, showing that the latter is considered on the same level as the elite officer of the Doflamingo Family. Vergo was only able to keep ahead of Law because he had the latter's heart at the time — a situation that immediately reversed after Smoker (reluctantly) helped Law to retrieve the organ.
He is also apparently quite fearless, as he allowed several Marines to get within close-range of him on Sabaody Archipelago, despite being a long-range fighter. During their stay at Sabaody Archipelago, the Kid Pirates and Heart Pirates were caught in a battle with a Pacifista. The end of the battle was unseen, but since they reappear during the Marineford Arc, it can be assumed that they either defeated the Pacifista or managed to elude it. Kizaru mentioned that the Heart Pirates did a good job at running away.
Sometime during the timeskip, Law has become so powerful and infamous that even the ruthless Marines of G-5 were deeply afraid of him. He had gained a bounty that surpassed Luffy's at the time, and brought a hundred pirates' hearts to the World Government, earning him a position in the Shichibukai. Law was able to battle and eventually defeat Smoker, a Marine vice admiral and a Logia user without getting himself seriously injured. He also defeated Vergo in one move, while before in the past was unable to even harm him. He is now strong enough to counter attacks from an Admiral and a fellow Shichibukai at the same time, as shown during his confrontation with Issho and Doflamingo.
Law is a very crafty and opportunistic leader and also a highly skilled strategist, being the only member of the Worst Generation to voluntarily rest in the Paradise half of the Grand Line for at least two months before entering the treacherous region of the New World, proving great caution and tactical preparedness. He obtained the title of Shichibukai in order to avoid detection of his actions and easily sail through the New World. While in Punk Hazard, Law secretly swapped numerous Seastone chains with ordinary chains as a future precaution that proved to be critical in allowing him to stealthily escape from Caesar's cage that is about to be exposed to the deadly Shinokuni gas.
As Vergo noted, Law concocted a multi-layered plan to cripple Doflamingo's Smile trade by destroying the SAD production facilities on Punk Hazard as well as abducting Caesar, the only person who knows how to create the unique substances. Through this plan, Law managed to force Doflamingo, an extremely cunning and resourceful pirate in his own right into a utterly disadvantageous choice of quitting the Shichibukai and facing the Admirals or keeping his position and face Kaido's wrath. He was able to fool Doflamingo into believing he killed him by swapping places with a foot soldier when the latter shot him repeatedly and retaliated when the latter's guard was down. When badly weakened, Law resort to tactically defeat Trebol, tricking the latter into letting his guard down to finish him off with his Sterben technique.
In addition to his Devil Fruit, Law has underwent an extremely rigorous combat training regimen under the Donquixote Pirates as a child, attaining incredible superhuman physical prowess. While still a twelve year old boy, he was already strong enough to throw Rosinante, a very tall and large man, by grabbing him by the leg. Additionally, he has the physical power to block Doflamingo's extremely powerful Overheat string which shook the Thousand Sunny with just his sword. He easily wielded Kikoku a sword as tall as himself with great speed, able to slice enemies faster than they can react and keep up with Doflamingo.
He has also displayed exceptionally great endurance, as he had his heart directly crushed to the point where he lost consciousness, only to recover shortly afterwards. In addition, he was also capable of enduring a prolonged brutal beating from Vergo which resulted in him becoming severely bloody before defeating him in a single blow once Smoker had retrieved his heart. Even as a child dying from from the incurable Amber Lead Syndrome, Law was able to keep up with the very harsh training regimen of the Donquixote Pirates where even adults could not keep up with. And when his disease reach a fatal stage, he could survive a ruthless beating twice from Vergo.
Even when he was defeated, and injured by Donquixote Doflamingo and Admiral Fujitora, as well as pinned to the ground, by Issho's Devil Fruit power, Law was able to quickly recover and escape.
During his second confrontation with Doflamingo, Law was able to fight him and, despite still wounded from their first encounter and even after having his right arm severed and brutally assaulted further, he was able to continue fighting and deal Doflamingo a severe wound with his Gamma Knife move. Even incapacitated by Trebol, he was still able to use his Devil Fruit Power to control his severed arm and even defeat the officer.
Law also has formidable skills in martial arts, having been trained in this aspect by Lao G. In the anime, Law was able to hold his own against Luffy, an extremely powerful fighter in a fist fight, when Breed forced Luffy to fight Law through the Peto Peto no Mi. With Busoshoku Haki, Law could block against Doflamingo's Goshikito with his arms crossed in a defensive stance. Even at age 13, Law could defeat both Penguin and Shachi, who were bullying Bepo, a mink who is a natural born fighter, impressing them to the point they swore loyalty to him.
Since childhood, Law was already well versed in medicine, having attended an academy for medical science, while his father, the best doctor of Flevance, personally taught him the more intricate procedures. Even after he joined the Donquixote Pirates, he still retain a profound understanding of medical science, as he was able to use Ope Ope no Mi to remove all traces of the Amber Lead inside his dying body. This was noteworthy as he was able to find a cure for the poisoning that was said to be incurable and live past the age he was supposed to die at. His medical aptitude was what led Donquixote Rosinante to conclude that Law was most compatible with the fruit, which prompted him to secure the Ope Ope for Law after he received information from both his brother and Sengoku of the fruit's present whereabouts at the time.
He earned the nickname "Surgeon of Death" due to his immense surgical skills in addition to his formidable combat abilities. He was able to simultaneously operate on both Luffy and Jinbe right after both of them barely escaped a murderous Akainu who inflicted brutal life threatening injuries that left them on the brink of death and was successful in treating them. The mere fact that he was able to stabilize Jinbe's condition strongly hints that Law's medical expertise is not limited to human anatomy alone (though human and fishmen share the same blood, so it is possible that they have similar anatomies). He later volunteers to find a cure for the children's condition at Punk Hazard, showing that he is also very knowledgeable in pharmacology. The fact he was able to apply pharmacology knowledge into his Devil Fruit powers to remove most of Caesar's deadly NHC10 drug out of the children's bodies, though not completely, is a noteworthy feat, something Chopper was even amazed by.
The spatial powers given to him by the Ope Ope no Mi allow Law to perform even the most complicated and difficult surgeries perfectly with great ease, as they allow him to cut a patient's body open and remove organs without damaging any tissues, leaving scars, or causing the patient to bleed a single drop of blood while removing any disease causing impurities as well as poisonous substances and narcotic drugs from the patient's body. This was demonstrated, off screen, during the conclusion of the Punk Hazard arc, during which he treated the children with a series of surgeries that involved cutting the childrens' bodies apart in a manner that initially made Chopper believe he had killed them.
As a boy, Law was able to remove all the poisonous amber lead inside his dying body curing himself of the Amber Lead Syndrome proving his capability to use the Ope Ope no Mi to treat even incurable disease. Law could also apply medical knowledge of anatomy into his Devil Fruit powers for combat, such as precisely removing important and delicate organs of powerful enemies such as the heart which would render them vulnerable to lethal harm such as death, proven when Law extracted Monet's heart with his power and gave it to Caesar, Caesar fatally stabbed Monet's heart, bypassing her defensive powers as a Logia user, effectively killing her, Law as well as Sanji and Bege was able to keep Caesar who is also a Logia user and a dangerous criminal under complete control due to having taken his heart hostage which is removed in a similar fashion, and the fact he used his anatomical knowledge to invent the Gama Knife technique on his Devil Fruit which could fatally rupture and destroy the internal organs of even a Shichibukai like Doflamingo further proving the fearsome way Law could actually weaponize his medical knowledge.
Law is the user of a Devil Fruit called the Ope Ope no Mi, which allows him to create a spherical territory of light blue aura. In this territory, he is capable of separating and spatially displacing anything and everything inside (including himself), referred to as that he can "operate" on anything within the spherical "operating room". Easily among the most versatile Devil Fruits around, with his powers, Law is capable of causing mass havoc within the area he controls. He can also use it for teleportation purposes. He has also demonstrated being able to apply his ability for medical purposes, as seen when he cured the giant children from their addiction brought by Caesar's drugs.
Law appears to have mastered his power to such a great extent, that he can even cut through someone who completely imbued their body in Busoshoku Haki.
The weakness of the technique seems to be the concentration required to use it; Law must gesture with his hands to centralize the effects upon its victims, which can allow an opening for a fast enough opponent, such as Vergo. His abilities also depletes his strength the more he uses them. And given Law's strategic nature, he seems to have a strong tendency to preserve every bit of his stamina in preparation before facing off against powerful adversaries, like the likes of Doflamingo, as seen when he consistently refused to use his powers to aid the Straw Hat Pirates as they made their way towards Green Bit. Other than that, he has the same standard weaknesses as all Devil Fruit users.
Law's offensive abilities lie in his swordsmanship. He has demonstrated himself to be extremely skillful in wielding his Nodachi Kikoku, a sword about as tall as he is. Even without using his Devil Fruit abilities, Law is capable of fighting even a Vice-Admiral such as Smoker, able to clash against his jitte with little effort and even block extremely powerful long range attacks such as Doflamingo's Overheat. In contrast to the ranged slashes of traditional swordsman, Law’s sword slashes don’t travel but simply provide the cutting effect while his spatial manipulation within his ROOM provides the range. Through spatial slicing, he can dismember people without harming them and attach separated parts in any manner he sees fit.
His swordsmanship combined with his Devil Fruit powers enable him to mutilate numerous people at once faster than they can react, apparently defeating Kin'emon a very powerful swordmaster who is capable of cutting steel and use fire enhanced slashes in this manner. He also was able to quickly defeat Tashigi, a very skilled swordswoman of the Marines, severing her sword in two, as well as taking down Scotch and his giant knife in one swift move. He also managed to mutilate Trebol, an enormous man and also one of the strongest members of the Donquixote Pirates.
His greatest swordsmanship feats shown so far have been defeating Vergo, where the wake of his slash was capable of cutting apart Caesar's laboratory and the surrounding mountains, and cutting a meteor in half.
He also managed to wrap the rope created by Donquixote Doflamingo's attack around his sword.
Law has shown great proficiency in Busoshoku Haki, able to block Doflamingo's Goshikito which is powerful and sharp enough to slice Issho's meteorite and also took out a large portion of the palace without getting injured at all.
During his battle with Smoker, Law was shown capable of bypassing the vice-admiral's Logia defenses thanks to his own Haki powers.
Kikoku is a large version of the typical Japanese sword type known as a nodachi. It has an oblong-shaped hand-guard coated with short white fur, sheathed in a black scabbard decorated by white crosses from the opening to the bottom, and with a small piece of red rope tied near its opening. Law appears to be quite skilled with it, being able to slice up targets from a distance (although this effect is attributed to his Devil Fruit power). Due to its size, Law usually carries this sword over his shoulder (in contrast to the other sword-wielding characters in the series, who either carry theirs on their hips or over their backs); yet in other times, he delegates one of his crewmates (namely Bepo) to carry this sword for him. Law was able to deflect Doflamingo'sstrings with his sword, which is noteworthy, as Doflamingo managed to effortlessly cut everything else so far.