Vinegar was a human-made preservative, used for pickling and flavouring foods. Vinegar contained acetic acid, which could kill Raxacoricofallapatorians because of their calcium-based biology. The most common users of vinegar against Raxacoricofallapatorians were several of the Doctor's friends, who used them against the criminal Slitheen family (TV: World War Three, Revenge of the Slitheen, AUDIO: The Taste of Death)
Mickey Smith had several vinegar based foods including gherkins, pickled onions, and pickled eggs in his pantry. Jackie Tyler used these in order to kill Sip Fel-Fotch Passameer-Day Slitheen, who had gotten into the house. It caused him to explode. (TV: World War Three)
Hannibal crossed the Alps by using vinegar to dissolve boulders. Harriet Jones was reminded of this when the Ninth Doctor told Mickey Smith to use vinegar against the Slitheen attempting to kill Jackie Tyler and him. (TV: World War Three)
When the Slitheen took over Park Vale Comprehensive School, the food went off as a side-effect of their efforts to turn off the Sun. Due to this, Clyde Langer brought in a cold chip sandwich as an alternative to the school dinners. Kist Magg Thek Lutiven-Day Slitheen, disguised as the teacher Mr. Jeffery, could smell the vinegar in the sandwich thanks to his species' sense of smell, which made him noticeably scared. This helped Sarah Jane Smith figure out that vinegar was the weakness of the Slitheen.
Sarah Jane and her friends arrived at the school armed with vinegar, Clyde and Maria Jackson sprayed some at Glune Fex Fize Sharlaveer-Slam Slitheen when he attacked them. Maria later threw the whole lot at the Slitheen when he taunted her, exploding and killing him. Out of vinegar, Clyde tried to use water to threaten the Slitheen, but they could tell it wasn't vinegar. (TV: Revenge of the Slitheen)
When Luke fell seriously ill due to the Rakweed plant brought by the Blathereen, later revealed to be Slitheen-Blathereen, Sarah Jane teleported to their ship in Antarctica. She was armed with jet-powered water pistol loaded with vinegar, ordering them to eliminate the Rakweed or else she would use it. The Slitheen-Blathereen had her believe they removed the Rakweed and persuaded her to lower her weapon, they then forced it off her and had her restrained. (TV: The Gift)
To the surprise of the Tenth Doctor, vinegar was among the stock of the restaurant on resort planet MXQ1, despite its operations being commandeered by the Slitheen. The Doctor used the threat of vinegar to ward off the pair of Slitheen who had disguised themselves as the Bluestone brothers. When the Slitheen guards attempted to collect customers for harvesting, Rose Tyler urged the diners to use vinegar to defend themselves, noting that it could be found in salad dressing. (AUDIO: The Taste of Death)