Possible Solutions:

The birds don't get an electric shock...

a) ... because birds are positively charged animals and can thus sit on the equally positively charged high-voltage lines.

b) ... because no electric current runs through a bird. There is not electric potential difference between the feet of the bird, which would be necessary for an electric current.

c) ... because, unlike we humans, birds have feathers and those allow the current to dissipate. An electrical current is generated but it is dissipated immediately.

d) ... because there is no current running through the birds. There is no difference in amperage between the feet of a bird. But this would be necessary for an electric current.