Intelligence
If one had thought that assassinations were a crude and messy affair, they could be right on both accounts if they didn't reference to the hits done by Varia. After all, violence did not equate to tastelessness or crassness.
If they did, the Varia would not have survived and been titled as Elite Assassination Squad. Their title alone showed that they were unconventional which then showed that they had an iron-hard confidence and trust in their abilities. After all, who would dare to proclaim their name to the world especially in their line of business. At the same time they were neither remiss nor stupid, the missions which had their signature flair were intended. On the other hand, missions of a covert nature were able to have no scent (to be claimed as natural deaths), mimic other assassins (to frame and cause discord) or to be rather inane and unprofessional in their killings (to be seen as an outlying case). To sum it all up, the Varia places much contemplation into their killings and not one move is done without intent.
And how would they be able to do so, if they were mere weapon-wielding idiots?
The answer is now obvious and simple, they just aren't. So, where does their strength lie in? Intelligence.
Intel, intellect, wit… (all the various words that are either the definition or tied to the word 'intelligence'), the Varia are definitely not lacking in this. As for the methods they apply, let's just say that they occasionally submit to the whims of their emotions or inherent nature. Interrogation or torture, it depends on their mood which they would like to carry out, but their success rate is 100%. After all, from their picky nature of only accepting missions with the success rate of 90%, you can tell they mean assured business. They have their goals and are willing to capitalize on their abilities and resources except for of course their lives and reputation.
Now then, what are in their skill set? Apart from the different sectors with the various flame abilities, they were all well-versed in multiple languages and weapons as the basis of their job requirement. From morse codes, sign languages to Italian, French, and English, they had the proficiency and eloquence of a native speaker regardless of their slightly telltale accent. They are also all adept at wielding bladed, blunt, projectile, liquid weapons, it is a matter of preference or need should they pick one method. On top of this, they all had upbringing of various sorts- no matter royal or peasant to be cultured with some form of art- music, dance, painting.
This is invaluable for espionage, to play the aristocratic nobleman, the demure lady, the deranged artist, the charming musician and many more roles. To blend in or to capture attention were the second nature of the assassins in Varia. Of course, there were certain characters that they were more inclined towards. Unsurprisingly, Lussuria as the fashion designer, Mammon as the shrewd businessman and Belphegor as the spoilt prince. These were roles that they frequently peak through their normal lives in Varia. On the other hand, Squalo was the fluent negotiator and Xanxus was the detached and intelligent boss. Of course these roles weren't far fetched as Squalo was trained to be Xanxus's right hand man and Xanxus was more than reticent yet cutthroat in his interactions.
Therefore, the Varia has the ability to manipulate their abilities for various mission needs. These needs are uncovered by detailed investigative research, silent and deadly as these seemingly minor and meager details weave into a lethal trap set for their target. The honeyed words, the bleeding stares were all picked out through the sifting of relevant information to pierce (prod and poke were too mild the term) the weak points of the target.
The assassinations were never done in a whim or carelessness. They were of planned meticulously through the painstaking and tedious work of gathering information before the time is right. Never let it be said that their assassinations were not a work of art- the vivid slash of blood on the carpeted canvas or the bare shadows of a once occupied room were all art strokes.
The rule of all assassinations is the wielding of intelligence.