Nasty is something that is "gross and sexual " or unhygienic" dirty is something that is something sexual that is inappropriate for polite conversation. Smutty means it's all low brow, unsophisticated and sexual. Erotic is high brow, sophisticated and sexual with out being explicit. Instead everything sexual is implied.

Wow , that's for us to discuss in private

Correct. You can say a dirty innuendo but it would be redundant. Many of these words can be used interchangeably, and often have overlapping meanings.