One of the most evident things about Hunter x Hunter is the sheer number and variety of characters contained in the show, not to mention a large fraction of them get a believable backstory. This applies to villains as well — considering the Yorknew City and Chimera Ant arcs alone, there are over fifty relevant antagonists.
Now, how many of these villains could Aang from Avatar: The Last Airbender actually defeat in battle, and who among them can overpower the Air Nomad protagonist, with or without the Avatar State? Aang is certainly going to have his work cut out for him in a few cases, while others would pose little to no threat.
Aang Could Defeat: Shalnark
Shalnark's Black Voice Nen ability requires him to pierce his opponent's nape with a little bat-shaped antenna, thereby acquiring physical control of his target. Aang's speed and reliance of Airbending for defense are just enough to avoid being struck by the needle.
Shalnark could go into Autopilot mode himself, in which his Nen takes charge of his body, augmenting it with incredible physical prowess, but Aang's Earthbending barriers can easily stop his opponent, followed by frozen Waterbending to trap Shalnark in place.
Aang Would Lose To: Hisoka Morow
There is no imaginable scenario in which Aang could triumph over Hisoka, simply because the latter would not allow the Avatar to unleash his full potential.
As much as Hisoka would like to wait for Aang to grow into a powerful adult before taking him seriously, a fight would be inevitable if these two forces ever clash. The Avatar State is certainly capable of defeating Hisoka, but is he going to let the battle get to that point? Unlikely.
Aang Could Defeat: Cheetu
Cheetu is all about his speed, and his incessant boasting about the fact reveals tons of personal insecurities. His Tag transports both him and the opponent into an inner dimension where the latter has to "tag" Cheetu to escape.
As Morel mentions, the Chimera Ant is far too new with his abilities, which makes his offense negligible and the only defensive move Cheetu has is running away. So, yes, in theory, the Chimera Ant could run away from Aang, but a head-on match will turn out in the Avatar's favor.
Aang Would Lose To: Meruem
Meruem, the Chimera Ant King, possesses a life aura whose radiance is immeasurable; his strength is proven when he successfully defeats the greatest Nen-user in the world, Isaac Netero.
Aang can try anything he wants — elaborate bending techniques, a fully conscious Avatar State — but he is going to end up defeated by Meruem. In fact, it can be argued that the Ant King will be able to destroy Aang with a single attack.
Aang Could Defeat: Pakunoda
Pakunoda possesses a fundamental knowledge of Nen, which makes her a lot stronger, faster, more intelligent than most people. Her Specialist technique, Memory Bomb, can be used to extract information from any target's mind as long as she is touching them at the time.
This is quite handy in the Yorknew City arc when Pakunoda saves Chrollo from Kurapika, but reading thoughts is not going to counter the devastating effects of elemental bending.
Aang Would Lose To: Feitan Portor
Avatar Aang would get the better of Feitan if the latter only uses his swordsmanship and speed, but the Phantom Troupe is terrified of his Nen ability for a reason.
The Avatar can control fire, but Feitan's anger-based Pain Packer generates a mini-sun whose heat is enough to liquefy rock, let alone his enemies. Although Aang can hold the Conjuration technique off for a short time, Feitan's aura only increases with the amount of injuries he receives in battle.
Aang Could Defeat: Uvogin
Uvogin is the strongest of the Phantom Troupe, in one case winning a three-on-one battle using his teeth and his voice; and his Enhancement-based Big Bang Impact has resulted in enormous craters and instant deaths.
Uvogin cannot be killed by Aang, even if the Avatar wants to, because his body and willpower are nigh-invulnerable. However, Aang would stop and imprison Uvogin, far more efficiently than Kurapika does.
Aang Would Lose To: Illumi Zoldyck
Illumi's Manipulation skillset is terrifying, at least from Killua's experiences being under his older brother's Nen control. The oldest Zoldyck son can perform all sorts of techniques, from hypnotizing people to physically controlling their bodies with his Needle People.
Aang needs to be aware of how assassins function in order to have a chance against Illumi, but as it stands, there is little hope that the Avatar would come out of this battle unscathed.
Aang Could Defeat: Yunju
Yunju is one of the more fearsome Squadron Leader Chimera Ants, with a predilection for brutality and cruelty. He is quite powerful, considering that Kite warns Gon and Killua not to take Yunju and his minions lightly.
But what damage could a mere centaur do against the Avatar? A couple of pinpoint Waterbending strikes would freeze Yunju to the floor, and that would be the end of that fight. There's no need for any other forms of bending, really.
Aang Would Lose To: Chrollo Lucilfer
Avatar Aang's knowledge of the four bending arts is profound, as is his control over the process of Energybending, but this is not going to be effective against Chrollo Lucilfer.
The leader of the Phantom Troupe has shown that he can handle offensive blasts from the likes of Silva and Zeno Zoldyck, and this doesn't even take into account his Bandit's Secret. Chrollo can swipe others' Nen abilities and manifest them himself, making a fight with him unpredictable at best. Aang will not know what hit him.