Here's my strategy.
I have caller id. If the phone rings, I
a. never run to it, esp. if hands in water, I'm in shower or eating.
b. caller id tells me if I want to answer it. If it's really important, the caller can leave a message. The nuisance callers never get to that point..
c. unplug phone if want to nap or just not be interrupted.

I don't get too many nuisance calls. Changing to a new unlisted number only means you a. get a lot of misdirected calls ( as I doubt there are any virgin numbers being assigned) and b. you have to notify ppl and, sure as shootin', you'll forget someone you'd like to hear from.

I also have anonymous caller block, but I doubt it works.