1) An oxidizing agent is one which itself is reduced i.e. it has a tendency to accept electrons.
2) In all the given ions there isppi−dpi back bonding.
3) In ClO−4 it ispi−3dpi,BrO−4 it is 2ppi−4dpi and in IO46− it is 2ppi−5dpi.
4) Here electrons from p orbitals of Oxygen are back donated into thed−orbitals of halogen atoms.
5) As you see the size of the d-orbital is increasing and hence the effective overlapping will be less. So, ClO−4 has most effective overlapping which means the desire for electrons in Cl is well satisfied by the back bonding which is less in case of BrO46− as here the overlapping is not so effective due to large size of the d−orbitals. So, Br can still accept electrons,i.e. it can get reduced more easily than the Cl and hence acts as a strongest oxidizing agent among Cl and Br. And I can get more reduced than Br.
6) So, order is: ClO−4<BrO−4<IO−4.