Why aren't Delta and Omega particles stable? Not only are they not stable their half-life is in the nanoseconds.  Why are they so different from protons?
 A: Delta half lives are around $5 \times 10^{-24}$, which is 11+ orders of magnitude less than nanoseconds. They are so short that one generally discusses the width ($\Gamma$) of the resonance, given in terms of the mean life ($\tau$) by:
$$ \Gamma \tau \approx \hbar $$
Deltas are the 3/2-isopin version of the 1/2-isopspin nucleon, roughly and excited state, and decay via the strong interaction (pion emission) without any flavor changing.
The Omega is stable via the strong interaction (and EM), so it has to wait for a weak decay to change one of the strange quarks to a down quark (see: Cabibbo Angle). The half-life is 1/12 ns, not quite "nanoseconds".
A: 
Why aren't Delta and Omega particles stable?

It is a general rule, that a quantum mechanical state decays to the lowest energy level allowed by conservation of energy and quantum numbers.
In the case of the Delta the lowest energy state is the proton, because it can decay to it via the strong interaction, conserving baryon number. In models beyond the standard model the proton can also decay, and there are experiments searching for such decays .
If you look at the Omega particle you will see that it is composed out of three strange quarks. Strangeness is conserved by strong interactions, and the weak interaction is responsible for its much longer lifetime to decay to lower energy states, by the weak decay of one of the strange quarks.
