Yeah even I agree that there is no universal definition for what is strong acid and what is weak acid.
The strength of acid and bases depends on the roles of the solvent used. The greater the tendency of the solvent to accept proton, the more will be the strength of the acid giving proton.
For example, acids like HCl, H2SO4 etc dissociate completely in water (solvent) as water accepts all their protons. Thus these acids are said to have equal acid strength (leveling effect). But the same acid when take in acetic acid(solvent), dissociate partially and act as weak acids.
Again acetic acid in water is a weak acid, whereas in the solvent ammonia it is a strong acid.