Dear Jiang,
I is understandable that you are having difficulty with these words as they do convey similar meanings. I will try to help you understand the difference.
First, normally the correct way to phrase the statement that you asked about is "He is standing under the tree" if you mean that the branches of the tree are over his head.
The opposite of under is "over" and the opposite of above is "below". Usually we use "over" to describe thinks that are directly above you and we use "above" to describe things that higher than you are but not necessarily directly above you.
Here are some examples of each:
It is nice to have a roof over your head.
Heaven is above.
He has a cloud over his head.
The sky is above and the earth below.
I hope this helps
