Worse, the strong force isn't really its own force at all - it's a special case of the color force, the force that binds quarks together.
That is what "The strong force" is. The force that binds nucleons together is sometimes referred to as the residual strong interaction, because of this.
Weak is weaker than EM. I can't think of anything it does other than beta-minus decay and some stuff in other decay chains.
Ah yes. Mistake on my part.
The weak interaction does actually much more than that, though rarely at regular energies. It can do many of the same things as the photon - you can have e+ e- pairs annihilating into a Z (and the opposite process of pair creation), absorption or emission of a Z, etc (hence why the whole electroweak idea - the Z boson is very similar to the photon in the standard model). W bosons are a bit more complicated but in essence they do the same kind of things.
So.. Tweaking the weak force might change decay rates? The whole random-quantum-fluctuation-interaction stuff is a bit of a mystery.
Tweaking the coupling constant (that is the actual name of "the force of an interaction") would indeed change the decay rate. This one at least is rather simple as, from memory, the decay rate is proportional to the square of the constant.
What if strange quarks were stable? What we call Xi minus and zero could then act as nucleons; the zero would act something like a heavy neutron, but a negative nucleon would be ... different. What changes to laws/constants would this need?
Hard to say. You don't really speak about the stability of the quark themselves, as they are never free. The fact is, only the proton is stable (or at least has a decay rate currently too long to measure). The neutron is not stable, with a half life of about 17 minutes, and it's all downhill from here. Why the neutron is stable inside a nucleus is a complicated issue, but the most intuitive notion I've heard on it is that because of the constant pion exchange (the carrier particle for the residual strong interaction), the protons and neutrons constantly change in the nucleus - a proton emits a pi+ and becomes a neutron, and a neutron absorbs it, etc.
The interaction responsible for the decay of baryons is (I think) usually the strong interaction, with the weak one in a smaller measure (from a cursory glance, anyway - less than 1% of decay products include neutrinos, which are a pretty good sign of weak decay). But the problem isn't so much the strength of the interactions as it is the fact that the proton is the lightest one. On a purely energy perspective, any baryon will end up as protons + electrons and neutrinos, because then, it cannot decay further (well, it can, but it is pretty unlikely).