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 the one with the highest ever shown strength; this was shown when Stefan, Damon and Klaus tried to immobilize him and failed.
Silas was an immortal rather than a true vampire and possessed a degree of Super Strength but was inferior to not only "normal" Vampires but that of the brotherhood of five, who's strength was probably more or less equal to that of a werewolf (untransformed), that said, Silas was still much more dangerous than even the Enhanced Original due to his illusions and greater mind compulsion which showed that even a powerful vampire of nearly 200 years like Damon who's strength would have been vastly superior to Silas' was no match for him as Silas easily compelled him to stop fighting, making super strength against him ineffective.
Werewolves also have super strength that grows over time but to a lesser degree with their age, compared to vampires. Untriggered werewolves are pretty stronger than human beings in general; this was seen in Brave New World, when Tyler was able to beat every one at arm-wrestling but Mason. Stefan realised that they were dealing with something new when he then played against Mason; he lost on purpose. They are relatively weaker than vampires while in their human form. This was seen when Caroline bested Tyler when he tried to force the truth out of her. However, during full moons, they turn to their wolf forms. They get far stronger and more powerful than non-original vampires during full moons. However, there hasn't been any scene with illustrable proof as to how strong they are in circumstances involving original vampires and non-transformed hybrids. It is unknown how they will fare against them in their wolf forms.
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. Damon the upper hand against Tyler 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. He took on all of Marcel's vampire army, and won. So, basically, don't provoke him because he will descend upon you.
A group of supernatural hunters endowed with enhanced attributes to make them more effective hunters, super strength is one of these attributes and is used effectively against vampires and hybrids. Connor was able to rip a Hybrid's head off with proper leverage, and Jeremy was able to lift two drums in each hand whereas Matt could not lift one with both hands. Jeremy was also able to fight Silas on even grounds and could of possibly won if not for the latter's immortality.