Super Strength is a supernatural ability possessed by vampires, werewolves, and hybrids. This, in addition to granting them great endurance, allows them to be stronger and more physically powerful than any human and possibly large animals. Super strength varies among users, depending on their age, species, and diet.
Vampires have super strength that gets stronger as time passes. The level of strength in vampires depends on their age and their diet - consuming human blood regularly makes them stronger than those that consume animal blood. Even transitioning vampires, have been shown to be several times stronger than they were before they turned. This was demonstrated in Blood Brothers when Stefan, not knowing his own strength flung his father in a reflex retaliation when he attempted to stake him. They're stronger in comparison to werewolves when not in wolf form. In Season 3 episode, Ghost World, it was clearly shown that Damon had greater strength than Mason while shovelling into the Lockwood cellar. The tables are, however, turned when werewolves are in their wolf forms, during full moons, as was shown on at least three occasions during Season 2. Vampires often use this ability in conjunction with their Super Speed to make quick moves with great force.
Originals are stronger than normal vampires mainly as they were created for the sole purpose of fending themselves off of werewolves; they're stronger than werewolves even in their wolf forms. Normal vampires are usually no match to originals, except with the element of surprise. This ability has been used to break necks and spines, and break and move heavy objects. Their impact can send people flying. Elijah has even displayed his strength as compared to a normal vampire when he decapitated a 500+ years old vampire, Trevor with his bare hand.
The enhanced original is the special form of vampirism seen in Alaric Saltzman when he was remade by Esther. He had super strength greater than the original hybrid Klaus. He was specially created for the destruction of the vampire race which could explain his level of super strength in a day of his transformation. The enhanced original is one of the highest ever shown strength; this was when Stefan, Damon and Klaus tried to immobilize him and failed.
It is, at this point, unknown if Silas has super strength in any way comparable to all the conventional vampires and originals. However, Silas seemed strong enough to hold Jeremy close to him to feed on his blood and was able to snap his neck. Silas just wanted to live forever and is unknown if he granted himself strength.
Ancient Vampires are stronger than originals and normal vampires because they are the first vampires in existence and over 4,000 years old. They were created with strength greater than any other supernatural in order to defend themselves. They grew stronger with age.
Hybrids have an extremely high degree of super strength. Newly formed hybrids are stronger than werewolves and even some vampires. They have a head start in strength due to their werewolf heritage. Although they are not as strong as a century old vampire and no where close to an original vampire, they can be considered stronger than those vampires that are not very old. It was seen in season 3 when Stefan and Damon could easily take down Klaus' newly formed Hybrids. Tyler had the upper hand against Damon when they fought in Homecoming.
Klaus is an original hybrid, which makes him stronger than all of his original vampire siblings. Klaus' strength is comparable to the enhanced original Alaric, but a little on the lower level. Just as an original is to a vampire, Klaus is to hybrids. This show of substantial strength has been demonstrated only by Klaus.