If by post hoc you mean several specific comparison tests, each with their own p values, then one of the simplest approach is to calculate the individual p values and use the p.adjust function in R. Say your individual p values are .01,.1,.2.,3,.02,.005, you type

p.adjust(c(.01,.1,.2,.3,.02,.005))

and R produces

[1] 0.05 0.30 0.40 0.40 0.08 0.03

which are those adjusted using Holm's method, which is the default.

Alternatively, you might first use different methods for plotting the residuals (like correspondence analysis). Given that if there are a lot of categories in each variable there will be lots of possible comparisons (and therefore lots of p values), it is not clear to me how to interpret that many p values (with or without adjustment).

Thank you, Daniel. I will give this more thought.