Even in the example you cite in your comment, which involves continuous rather than categorical variables, it's not clear that the centering gains anything. In R, for your case you simply would write something like lm(y~ x1 + x2*x3)
to get both main effects and the interaction for x2 and x3. The "*" here isn't an arithmetic multiplication, but rather an instruction to determine both main and interaction effects. In the default treatment contrasts used by R, the main effect for x2 will be the influence on y of changing x2 from 0 to 1 when the value of x3 is 0, and the interaction term will be the additional influence of x2 (positive or negative) when x3 is 1 instead.
Interpreting interaction terms is actually quite controversial and the literature is loaded with contradictions. My comments are based on a close reading of Aiken and West's book Multiple Regression which has one of the best methodological breakdowns for dealing with interaction terms that I've ever read. More recent papers (e.g., Understanding Interaction Models: Improving Empirical Analyses by Brambor, Clark and Golder, Political Analysis, 2006) aren't anywhere near as rigorous, contradict solidly documented A&W findings and add to the existing confusion.
First off, introducing an interaction shifts the interpretation from a main effects only model interpreted at the means of the Xs to a model with interactions that are interpreted at zero. This suggests mean centering your variables before taking an interaction term. The coefficients and std devs don't change, but the interpretation does.
Next, the main effects for the X's serve only to adjust the location of the intercept on the y-axis. It doesn't matter for the interaction term whether the X's are 0 or 1.
This is all a long way of saying that your suggested calculations need more information. In other words, it's not enough to assume that Y changes by '2' if the X2 coefficient, 'c,' is 2 since the effect of X2 is a conditional adjustment to the intercept. So, the impact on Y of X2 is not '2' when X2=1, it's 'a + 2'. Similarly for the calculation of the interaction between X1 and Z, it's not about shifting Z by 0.25 SDs. The full equation for estimating Y when X1=1 and Z=0.25 would be:
Ytilda = a + b + (0.5 * 0.25)
which would not equal 0.0125.
Best Answer
When you discuss the interaction you don't discuss it in terms of what happens to y but what happens to a1 and a2. If it's positive then as a1 increases a2 increases. If it's negative then as a1 increases a2 decreases. Interactions are about differences in effects. The slopes in regression are the effects and so it's most efficiently discussed in those terms.
Once you consider the foregoing you can understand why many say that main effects don't mean anything when there is an interaction. I don't agree with that as a generalization but certainly there are many cases where it's true.