Personally, I think, the subject of too many, or perhaps, too few, commas is subjective, and, if you think, and think very well, about it, you will agree.
Anyway, the first and the third commas are fulfilling this role:
As a bracketing (or isolating) comma to mark off a weak interruption of the sentence so the sentence flows more smoothly.
For the second comma, it's due to the way addresses are normally written in a single sentence, or even in multiple lines. Commas are used to separate each line of the address from the next, though this practice may be falling out of fashion.
The last comma seems to be a literary device used in the context to indicate the humor in the sentence: the addition of "thank you very much". By adding this, the author is trying to indicate the extend of pride the Dursleys have. They are immensely proud of being normal and abhorrent of all kinds of abnormality in others. They are so proud that if you think they are not normal, they will say you're out of your mind. Basically, the function of "thank you very much" is to be a humorous interjection indicating the amount of pride.
Normally, the conjoining of two barely related sentences would be done with a semicolon. However, the author chose to use a comma here, as a semicolon would break the sentences even further, losing their humorous value.