"I am done" or "I have finished" or "I am finished" or "I finish"

I was trying to say the following and got bewildered with the different choices.

I have "To Kill a Mockingbird" on my list. I will write you about it when I am finished reading it.

I have "To Kill a Mockingbird" on my list. I will write you about it when I have finished reading it.

I have "To Kill a Mockingbird" on my list. I will write you about it when I am done reading it.

I have "To Kill a Mockingbird" on my list. I will write you about it when I finish reading it.

I am not sure which one to pick. I am confused with the exact meanings of these various choices. Could someone also shed some light on what meanings the different tenses convey in a context like this.

All your four choices are acceptable in daily use. But technically, cakes are done and people are finished. Also, in proper English usage, I have finished is preferred over I am finished.

So, in that sense only the following (from your list) are correct:

I have "To Kill a Mockingbird" on my list. I will write you about it when I have finished reading it.

I have "To Kill a Mockingbird" on my list. I will write you about it when I finish reading it.

You could also use the following alternatives:

I have "To Kill a Mockingbird" on my list. I will write you about it when I finish it.

I have "To Kill a Mockingbird" on my list. I will write you about it when I will finish it.

I have "To Kill a Mockingbird" on my list. I will write you about it when I am through with it.

I have "To Kill a Mockingbird" on my list. I will write you about it when I am through reading it.

I have "To Kill a Mockingbird" on my list. I will write you about it when I am through with reading it.

I have "To Kill a Mockingbird" on my list. I will write you about it when I complete it.

I have "To Kill a Mockingbird" on my list. I will write you about it when I have completed it.

Also, if what you are writing is not colloquial, you should write I will write to you instead of I will write you.