Think about the state of the atoms in the compound and where they can go from there:
$\ce{I2}$
In this molecule, the iodine atoms have $0$ oxidation state, and are easily reduced to the very stable $\ce{I-}$ ions, with $-1$ oxidation state. This means this compound is capable of reacting as an oxidizing agent.
$\ce{BrCl}$
Likewise, in this molecule, the bromine and chlorine atoms have $0$ oxidation state, and are easily reduced to $\ce{Br-}$ and $\ce{Cl-}$ ions, which both have a $-1$ oxidation state. This means this compound is reacts as an oxidizing agent.
$\ce{HIO4}$
The halogen oxyanions ($\ce{F^{(I)}O- ,\ Cl^{(III)}O- ,\ Br^{(V)}O3- ,\ I^{(VII)}O4-}$), and really any oxyanion for that matter, have the marked ability to act as either oxidizing or reducing agents. These anions can accept electrons on the central atom in exchange for bonds to oxygen, acting as an oxidizing agent. They can also also accept additional oxygen bonds to the central atom, acting as reducing agents. Of course there is a limit to how reduced and how oxidized an oxyanion can become, but what I am trying to get across is that as a whole these species can act either as an oxidizing or reducing agent.
$\ce{NaBr}$
Here the ions exist as $\ce{Na+}$ and $\ce{Br-}$, which have $+1$ and $-1$ oxidation states respectively. Here, $\ce{Br-}$ is unable to accept any more electrons and can only donate them to form $\ce{Br2}$, making it an effective as a reducing agent. It can also be oxidized from $\ce{Br-}$ in the presence of $\ce{O3}$ to $\ce{Br^{(V)}O3-}$, and is still acting as a reducing agent.