Can I mix different data transformations in the same model? I assume it is OK to mix different data transformations in the same analysis. I've had to transform some variables to squared and some to cubed in order to meet normal distribution requirements. I'm assuming that it's OK to then use the transformed variables together for regression analysis?
 A: In addition to the excellent points made by @gung and whuber, consider what the model will mean once variables are transformed. It would be nice if you could tell us the context of the problem but.... Suppose it is, in fact, the case that the residuals are not normally distributed with untransformed variables, but OK with various different transformations of the variables. Will the result be sensible in your field?
OLS regression assumes normality of the error. Sometimes, it is better to use a different model, rather than force the data to fit the OLS model. There are a lot of alternatives. Again, if you tell us what you  are trying to do, we may be able to suggest some. 
A: From your question, I wonder if you are referring to transforming your covariates.  It is important to realize that regression models do not make any assumptions about the distribution of your covariates, but only about the distribution of the residuals (that is, not about the distribution of the response variable per se either).  
Of course, it is OK to transform your covariates, and to use different transformations with different covariates.  But this is done to fit a model with a curvilinear relationship between the covariate and the response variable, not to normalize the distribution of the covariates.  
If you do transform some covariates, there are a couple of things to remember:  


*

*you need to include the untransformed covariate as well (see here for more discussion of this)  

*if you include interactions between that covariate and others, you need to include interaction terms composed of all of the corresponding covariates, e.g.:
$$
\hat{y}=\hat{\beta}_0+\hat{\beta}_1x_1+\hat{\beta}_2x_2+\hat{\beta}_3x_2^2+\hat{\beta}_4x_1x_2+\hat{\beta}_5x_1x_2^2
$$

