In the case of both are strong, I can see why it's irreversible, because the acid is very willing to give a proton and the base is very willing to take one. Now here are my two main questions:
In the case of both are weak, we say the reaction is reversible. Does this mean the reaction happens then the products react again to give reactants, or that the reactants don't run out and the reaction doesn't happen at "full potential"?
In the case of a reaction between a strong base and a weak acid (or the other way around), why is it always irreversible? I mean since one of them is weak, shouldn't it give out an unstable product which is willing to react again, like
$$\ce{CH3COOH + OH- → CH3COO- + H2O}$$
The $\ce{CH3COOH}$ is a weak acid. The $\ce{CH3COO-}$ isn't stable so shouldn't it react again?