Hello, As far as I know that limma pipeline should work with normal distribution of counts. However, I couldn't find anything that says explicitly what is the expected distribution of voom transformation? Do I just assess the suitability of the method with just the voom mean-variance plot?

Most of the distributions the tutorial and documentations I have followed resulted in densities that are similar across all sample and roughly log-normal distributed. If I plot the logCPMs' densities before and after the transformation I still get muti-modelus DIFFERENT distributions?

No, there is no distributional assumption about the matrix of logCPM values. limma makes no assumption about the distribution of genewise expression values.