What test should I used? - Two categorical IVs and one categorical DV with three levels

Dear members,

I have two nominal IVs (both have two levels, O/X) and one ordinal DV with three levels.
I am also interested in the interaction of the two IVs.

So my question is 1) whether it is correct to run a multi nominal logistic.
2) Also, if I create an interaction variable (IV1 X IV2), how I can interpret the results?
(currently I have four conditions, but if I create this interaction variable, only one condition will be 1 and the other three will be 0, right?)

Thanks a lot in advance.
Hope you all have another great week.