How to define text css style in my themes folder to work with wysiwyg editor? Bold text and Italic text are not working in ckeditor and I think it is because I have sites/all/themes/mytheme/styles/mytheme.css somehow not communicating with it.

Other text formats like strikethrough and underline are working fine for ckeditor.

So do I need to declare a property in mytheme.css to allow the editor to work?

I don't have the eric meyer reset file included or anything , just the add on css changes I made to my theme but don't see how that is stopping the strong and italic tags from not working because my changes were made for specific div ids.
i usually add a separate .css file for the editors, this is only possible via the WYSIWYG module, in the settings of that text-format.
you can even add special classes and block-formats the user can choose then.

to see what's happening, you can inspect the editor normally in your browser, and should see the problem.