I already know that before using LinearModelFit, it is not necessary to transform the values of continuous variables into normal distributions. But I don't know if I need to transform the values to normal distribution before using the ANOVA package. I hope someone can help me clear up my doubts.
Fit your model, and before you look at the results, extract the residuals and put them in the QuantilePlot function. If it is roughly a straight line, then they are sufficiently Normally distributed.
Note that as the previous poster implied, an ANOVA is also a linear model and you can fit it using LinearModelFit using the NominalVariables option to indicate your categorical predictor(s). The Analysis of Variance package just gives you a few extra options. But the nice thing about LinearModelFit is that you can mix quantitative and categorical predictors (an ANCOVA).
What one is concerned about is if the residuals of the fit have approximately a normal distribution when fitting models with LinearModelFit or the Analysis of Variance package. The predictor variables (which used to be known as "independent variables") as assumed to be known and don't have distributions.
If you have a sample dataset and proposed model, it would be easier to address your question.