Yes, you can nest strong tags and the more you nest, the stronger it becomes. Although I'd say beyond 2-3 nested is extraneous.

The relative level of importance of a piece of content is given by its number of ancestor strong elements; each strong element increases the importance of its contents.

Source: HTML 5 spec

Some modern user agents will apply font-weight:bolder; to strong , though since it's already bold you won't really notice a visual difference. If you want, you can apply a rule such as the % so nested strong elements become larger, as indicated in the other answer.

Some screen readers might dictate the word out more loudly.

Seems like JAWS/Window Eyes screen readers don't indicate importance, according to this.