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.
Trafalgar Law is shown to be a very crafty and opportunistic leader, even for a successful pirate captain and a former "Supernova"; despite being regarded as one of the most powerful pirates of his generation, Law was the only one of the group to voluntarily rest in the "Paradise" half of the Grand Line for at least a couple months, rather than immediately enter the treacherous New World region, indicating a great deal of caution and tactical mentality. He also demonstrated this by replacing a lot of the seastone chains on Punk Hazard with steel ones and came up with a plan to quickly and stealthily escape from the cage he was trapped in. He was able to make a plan to retrieve the substance known as SAD, and his only miscalculation was Vergo, a man who was able to beguile the entire Marine organization, including the observant Smoker. He even managed to force Doflamingo, an extremely cunning and resourceful pirate in his own right, into a lose-lose scenario of either quitting the Shichibukai and face the wrath of the Admirals or stay and face the wrath of Kaido. 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 retaliate when his guard was down. When severely weakened Law resort to tacticality to defeat Trebol, tricking the latter to let his guard down to finish him off with his Sterben technique.
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.
In addition to his Devil Fruit, Law has sufficient physical strength and tactical prowess to duel on equal terms against Smoker and his jitte. Additionally, he has the physical power to block Doflamingo's Overheat string which shook the Thousand Sunny with just his sword.
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 beating from Vergo which resulted in him becoming severely bloody before defeating him in a single blow once Smoker had retrieved his heart.
Even when he was defeated, and injured by Donquixote Doflamingo and Admiral Issho, 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 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 able to use his severed arm and even defeat the officer.
Since childhood, Law was already well versed in medicine, having attended an academy for medical science, while his father, the best doctor of Flevance, taught him the more intricate procedures.
He earned the nickname "Surgeon of Death" due to his surgical skills in addition to his formidable combat abilities. He appears to be considerably skilled as a doctor, as he was able to treat Luffy and Jinbe right after both of them barely escaped a murderous Akainu that left them on the brink of death. 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, implying that he is also versed in pharmacology. The fact he was able to cure the children of Caesar's deadly NHC10 drug, though not completely, is a noteworthy feat, something Chopper was even amazed by.
The powers given to him by the Ope Ope no Mi make surgeries easier to perform, 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. 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.
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 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 Donquixote, as seen when he consistently refused to use his powers to aid his Straw Hat Allies as they make 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, demonstrated by his expert use of a sword about as tall as he is, though he is seen being able to defend himself without it by using his Devil Fruit abilities. 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. He can dismember people without harming them and attach separated parts in any manner he sees fit.
His proficiency is enough that he was able to clash against Smoker's Nanashaku Jitte with little trouble, and combined with his Devil Fruit powers he has repeatedly shown being able to mutilate people faster than they can react, apparently defeating Kin'emon in this manner. He also was able to quickly defeat Tashigi, a skilled swordswoman of the Marines, severing her sword in two, as well as taking down Scotch and his giant knife in one swift move.
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 is stated by Luffy to have Haki. The full extent of his ability in using it has not been revealed, but he has displayed enough proficiency with Busoshoku Haki to block Doflamingo's Goshikito which took out a large portion of the palace.
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.