Pearson's correlation coefficient is a measure of linear dependence of two continuous variables.
Your data is categorical so Pearson's and other measures of correlation do not apply.
Instead, it seems that you might like to build a contingency table of counts and apply a Pearson's chi-squared test for homogeneity/independence of multiple categorical populations.
I described how to do that in a thread here:
Also, it seems that you are interested in the strength of the association.
A simple possibility is just to look at the differences/residuals between the observed and expected counts from which you computed your chi-squared statistic. But, these residuals are hard to compare between cells because they have different ranges. If you just have a 2 by 2 table, you could compute the odds ratio for each of the cells which has a standard range. But, if your table is bigger, using odds ratio gets complicated. Another possibility is to standardize your residuals like this:
standardized residual for a cell =
( observedCount - expectedCount ) / sqrt( expectedCount * (1-rowProportion) * (1-columnProportion) )
Since there are so many ways to analyze categorical data, if you could describe the goal of your analysis in more detail and provide a packaged workbook with some data for me to work with, I could help you better.