"Have a look" vs. "Take a look"
Solution 1:
The difference between "have a look" and "take a look" is geographical rather than semantic. The former phrase is usually used in the UK, whereas the latter is usually used in the USA. (I am an American who has lived in the UK for 24 years.)
Solution 2:
If I really wanted to stretch my imagination, I might see "Take a look" to be just a smidgen more aggressive sounding.
I think for all practical purposes they are equivalent in meaning, as they would be for have/take a shower, have/take a drink, etc.