Hi noskaga,
The procedure you're describing, centering a variable, is the default option in JMP for situations in which you are fitting powers or interactions between variables. This process, also called "Centering Polynomials" (which is the option name in the Fit Model dialog under the top red triangle), centers each variable before operating on it (through powers or cross-products with other variables) so that the lower order terms are unconfounded with higher-order terms, and maintain an easy interpretation (the "average" effect of a variable assuming other variables are held constant at their mean).
For models with a single variable, or one with no interactions or powers, centering will have no effect on the coefficients (except for the intercept of the model). Odds-ratios are thus unaffected (and this should square with intuition: shifting the mean of the predictor does nothing to change the relationship that predictor has with the response other than the change the "level" of the response at 0, the intercept).
To manually center numeric variables you can use Analyze > Distribution, specify one or more numeric variables, and hit OK. Then select the Red Triangle (next to the variable name) > Save > Centered. If you have many variables, hold down the control key (or command if you're on a mac), then click the Red Triangle (for any of the variables) > Save > Centered, then let go. This will broadcast the command so you save centered versions of every column you have in Distribution.
I hope this helps!
Julian
