What are the 'distances' among the major English dialects?

Have a look at this highly relevant paper:

Towards an automated classification of Englishes
by Søren Wichmann and Matthias Urba
from the Max Planck Institute for Evolutionary Anthropology (Leipzig)

Have e.g. a look at the tree-like structure on page 4, Fig. 3.1. (unfortunately the referenced paper therein doesn't seem to be available publicly).

As an Australian, AmE, CaEn, NzEn, EnEn, ScEn, IrEn, ZaEn all sound quite "different".

• Tv personalities from America pretty much sound the same regardless of whether they are east or west coast. The same is not true however of the average american in the street.
• I'm not sure how you can't spot a Scot, especially one with a very heavy accent, as they are quite different.
• Cockney is also easy to spot, just look out for the rhyming and "nonsense words" they insert.
• New Zealand English is also quite different from Australian English, theres no confusion in spotting a genuine kiwi. As an example "six" becomes "sex", while "Fish and chips" becomes "Fesh and chups".