And where does God get his morality?
God created human morality.
Is anything God does automatically good...
Good for Him
...or does he himself adhere to some external standard of goodness?
His standard is his own Good pleasure.
If the latter, then there's no problem. Atheists can adhere to the same standards you imagine your god follows.
In a sense I guess they could and do adhere to some of the same standards, but as humans we fall short of these standards. In fact we fall short of even our own standards.
If the former, then how is that any different from "might is right"?
In God's case (as King of everything) might is right.