Acid "strength" is not a well-defined quantity. There are several "strong" acids, acids in which almost all of the molecules will dissociate in water. These include hydrochloric, nitric, sulphuric, perchloric, hydrobromic, and hydroiodic acids, and possibly some others. They corrode things because they produce hydrogen ions, and hydrogen ions will react with anything that is more electropositive than hydrogen (such as almost any metal).

That said, there are some other acids, like hydrofluoric acid, that aren't so powerful as acids, but are very corrosive for other reasons (in the case of HF, because of the fluoride anion).