Which conjugate base is stored in these: (1)ClO- (2)ClO2^- (3)Clo3- (4) Clo4-?

Strong acid or base means it ionizes completely in water. It has nothing to do with concentration or corrosiveness. There are seven strong acids:

Sulfuric
Nitric
Hydrochloric
Chloric
Perchloric
Hydrobromic
Hydroiodic

It's easy to remember the list because there are three of the most common industrial acids, three "chloric" acids, three "hydro" acids, and they all make a clumsy "7" on the periodic table.

There are dozens of strong bases and hundreds of "almost strong" bases.

Strong acid = weak conjugate base. That means -Cl, -ClO2, and -ClO3 are weak conjugate bases. So -ClO4 is the only choice not ruled out, so that is the answer.
en.wikipedia.org/wiki/Chlorine#Chlorine_oxoacids_and_oxyanions