1. When I was thirteen, I read a story of a man like me.

2. When I was thirteen, I read a story of a man like myself.
[Which one is right? are both okay? Can we use 'myself' as in #2?]

There is no clear rule on this one. I think the objective form (me) is preferable. The reflexive form (myself) is okay if it refers to the identical subject (I), so it's not unacceptable. I do think "me" is preferable. "Myself" is so commonly used, though, it's becoming acceptable.