The r and r² values seem to be correlation coefficients and coefficients of determination that comes from the relationship between each axis of the final ordination space and each of the variables in your main matrix. This is commonly used to assess which variable is more responsible for the differences observed in that gradient created by the ordination (NMS1, NMS2..).

Using categorical variables would require a distance measure that deals with these variables. You should carefully choose this distance, based on the nature of your data (only categorical, or mixed variables), and it will probably be a different measure than that used for numerical variables only. Thus, the result would be different from that of your actual ordination. To assess which variables are more important to the gradient of each axis, one option would be using Intraclass Correlation between your grouping variable and the scores of the NMS axes.

Although this can provide a meaningful result. I do not recommend you to use NMS scores in this situation, due to the non-parametric nature of the analysis.

The most important step would be the choice of the distance. I suggest you use Gower (if mixed variables) or a distance that deals only with categorical variables. Then, you can apply a metric-MDS, and try to identify which variable is more important to each axis of your ordination. Depending on the nature of the relationship between one axis and each variable (numeric-numeric or numeric-categorical), you use Pearson (or Spearman, preferably) coefficient or Intraclass Correlation. I am quite sure that Pc-Ord does not allow you to do that, and using R is a better option.

Finally, the "stress" is a measure of the quality of your multivariate space, but it seems that this p-value is a significance test, achieved by compared to the observed stress with those generated by randomizations. I just can not tell you if it is supposed to be > or < 0.05 to be significantly good.

From the questions that you have, it does seem like it would be better to use a constrained form of ordination, such as Canonical Correspondence Analysis, which is also available in the programme PC-Ord.  In NMS the configuration of the sample objects is determined independently of the environmental variables and the r and r2 are only calculated afterwards. In constrained ordinations such as CCA the environmental variables that explain your dataset are already part of the analysis from the outset and this is therefore more suitable if you have specific questions about explanatory variables.

In CCA you can incorporate categorical variables beforehand by including all categories as separate variables giving each sampling object a value of either 1 or 0 to indicate the category that the sampling object should be allocated to. In the programme CANOCO you can show the nominal variables separately from the other explanatory variables as each category will be indicated as a point in the ordination diagram that represents the cluster centroid of all the sample objects that belong to that category, but I don't think PC-Ord has that option so there each of the categories will be represented by an arrow, just as an ordinary explanatory variable.

The Erwin's answer suggests a better approach than mine. The CCA allows for controlling the categorical variables previous to the construction of the ordination space.

However, I suggest you a final approach. Use your original NMS to see if there is any pattern suggested by the ordination (constructed without the categorical variables, only the quantitative). In other words, use the result of the NMS to see if the groups are separated in the multivariate space. To test if this observed difference is significant, considering your categorical variables, use a PERMANOVA with two factors (slope and relative elevation). This analysis is a permutational procedure robust enough to deal with any issue regarding the assumptions that most statistical tests have.

I know that Pc-Ord does this PERMANOVA. I am not sure if it allows for more than one factor. That is why I strongly recommend you to use R.