Your problem is quite nice explained in Wikipedia (acid strength). Also all factors that influence acid strength are discussed.
But one sentence in wikipedia is not true: " and sulfuric acid (H2SO4). In aqueous solution, each of these essentially ionizes 100%". Sulfuric acid is strong, but only loosing the first proton, and may be treated as completely ionized (for student calculations within 5% error) only for concentration ~10-4 or less (since K2). And a few, relatively common, strong acids are missing, namely H4P2O7, HMnO4, H2CrO4, H2Cr2O7.
In this article also super acids (with wikipedia link) are mensioned. HClO4 is treated as superacid.