OPINION OF
'Opinion of' is usually used to express whether you feel positively or negatively toward something.
"What is your opinion of American people?" "My opinion of you is very good." "He doesn't have a very good opinion of people who cheat."
OPINION ON
This is used for general ideas and beliefs. If somebody asks "what is your opinion on _____," they are asking you to fully explain your view on an issue.
"What is your opinion on the current political situation in America." "My opinion on climate change is...."
OPINION ABOUT
This is not used very often. 'Opinion about' is often used to say whether or not you have an opinion.
"I don't have any opinions about America since I've never been there." "I have strong opinions about how people should raise their children!"
That is my best explanation. I hope it helped a little!