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.