I'm sorry, I had replied previously to the wrong post, let me revise my previous answer (which I have now deleted). For an unadjusted test, you could simply use a chi-squared test (both outcome and predictor are categorical). Adjustment will be much more difficult with a non-ordered categorical outcome. There is a logistic regression variant that can be used (not ordinal, but "mlogit"), but I actually don't recommend it...maybe collapse/dichotomize the outcome? I think that will get you a cleaner question and result...BUT this really deserves more discussion, so just take this as a teaser.