I agree with chuck m about opulent. I don`t think the word can be used to describe people, just surroundings (I`ve never heard it used as to people).

I`ll do sort of what they do in German in classifying words, by sort of ranking them. Rich and wealthy, are synonymous, but I think it is helpful to keep this in mind, 

Rich= colloquial, a sort of low-level word a 5 year old would know, but it´s used by everyone, so there`s no stigma to using it. It´s sort of street-level. 

Wealthy= a notch above rich. A bit more sophisticated a word. Not terribly so, but just a bit more elevated speech. Everyone is going to know it, but if you use it instead of rich I think you`ll sound more educated and more grown up. 

Affluent: I would rank affluent at the top of the ladder. It is a much more educated-sounding word. 

To most people, rich, affluent and wealthy are generally the same thing.

Opulent, is more associated with describing the surroundings, furnishings within a room or the overall level of luxury. For instance, the homes in Newport Rhode Island are the most opulent I have ever seen. Beautiful art work, gold-plated this and that, crystal chandeliers, etc. That sort of thing.