First of all, I must say this is a homework question. The complete question includes particles like $p$, $e^-$, $\Lambda$ and $\Omega$.
It's pretty easy to understand why $\Omega$ and $\Lambda$ have to decay weakly; $\Omega$ has three $s$ quarks so, no other baryon to turn into without changing strangeness. As for $\Lambda$, it is the lightest baryon with unit strangeness.
But when it comes to, for example, $\Sigma^0$ it can decay to $\Lambda + \gamma$. And while this particular process doesn't come from a strong interaction, I can't think of any reason why a process like $\Sigma^0 \rightarrow \Lambda + A$ where $A$ is a strangeless particle can't be possible. I'm not sure if the reason should be that there's simply no particle A that can fit that decay. The mass difference between $\Lambda$ and $\Sigma^0$ is pretty small, so maybe that is the case, but it sounds a little bit vague. Am I missing something?