Hi Murali,
I'm sorry for the inconvenience of accessing the files with Office Web App in browsers of Mac system.
Appreciated your detailed description, I would like to collect some information to narrow down of the issue.
1. Access the files with Office Web App in other browsers of a different computer to see if they can be accessed properly.
2. When does the issue occur? Do you make any changes about the settings on the computer before the issue occurs?
3. Are you a service upgrade user? Could these files be opened properly with Office applications?
4. About "It is worse in chrome. It won't open any file", do you get any error messages? Could you provide a screenshot about it?
Based on the current situation and the article about software requirements for Office 365, would you try upgrading the Safari and Chrome browser to the latest version? After doing that, please check to see if the issue persists.
Thanks,
Ida Qiu