I performed a Categorical Principal Components Analysis in ordinal data and I created 3 dimensions. Should I use the component loadings or the object scores, as my new 3 variables?
You probably had several ordinal variables, so your objects were described by several traits and you wanted to collapse this long description into few new traits. You succeeded an now your objects are described by 3 new traits.
This description is in object scores. Component loadings tell you how original variables were transformed to new ones.
So you should use object scores (I guess, since you write nothing about what you actualy want to do).