Teach has an immense amount of superhuman endurance and possesses tremendous physical strength even for his comparable size, which is demonstrated when he seriously injures Luffy and Ace, both who are exceptionally strong and powerful in just one hit, sending them both crashing back with incredible force and distance.
Blackbeard has eaten the Logia-class Devil Fruit Yami Yami no Mi.
Similar to a black hole, the user can absorb things inside a vortex. It seems that it does not completely compress and annihilate that which is sucked in as an actual black hole would do, but rather creates some form of space where things are stored. Blackbeard was able to suck an entire city into it and, when eventually regurgitated, everything expelled was reduced to scraps but not completely destroyed. The guards of Impel Down that Blackbeard sucked in also survived, although they were heavily wounded and in shock.
The most unique and frightening advantage of the fruit is that the user also has the ability to nullify the powers of other Devil Fruits by simply touching the user and draining them of their abilities. All types of Devil Fruit, be it a Paramecia, Zoan or Logia, are affected by this, though Logias are most affected as they can no longer become intangible by transforming into their respective element. This nullification truly seems absolute, as though the Devil Fruit users had never gained their powers at all.
The major strength of this particular fruit, the darkness the user turns into that swallows up everything, is also its major weakness. Since the darkness also absorbs attacks, the user of the fruit is still vulnerable to attacks, which do not pass through the darkness they turn into. If they fail to absorb an attack in time, the user can be hurt like any other normal human being or even more, as stated by Teach.
In addition, while the ability to nullify Devil Fruit abilities is very powerful, the user must actually touch and remain in contact with the victim for the effects to remain constant, meaning that if the victim is somehow separated from the user’s physical touch they will quickly regain their Devil Fruit abilities.
Blackbeard has become the first and, so far, only user to wield the powers of two Devil Fruits at the same time. Through unknown means, he acquired the extremely destructive powers of the Gura Gura no Mi from the dead body of Whitebeard and is now able to create earthquakes like his old captain. Marco speculated that this was possible due to an unstated peculiarity unique to Blackbeard himself, having to do with an “atypical body structure” of some sort.
With the newly acquired powers of the Gura Gura no Mi, which is said to be the strongest Paramecia-type Devil Fruit, Blackbeard can create shock waves by shattering the air itself, creating devastating earthquakes that can destroy the Marineford main building itself. He can also focus his quake powers into a “quake bubble” on his fist, greatly increasing the damage in a single punch.
With the power of darkness (Yami Yami no Mi), which “reduces anything to nothingness”, and the power of quakes (Gura Gura no Mi), which “brings destruction to everything”, Blackbeard claims himself to be truly invincible and the strongest of them all. During the two years, the Blackbeard Pirates went on to hunt down powerful Devil Fruit users to kill them and absorb their abilities, thus Teach (and possibly his comrades) has likely added more abilities to his arsenal.
Teach has mentioned Haki on multiple occasions though it is unknown if he can use it.