Check the Tiny MCE developers guide for information on how to define styles that can be selected by the editor:

http://world.episerver.com/Documentation/Items/Developers-Guide/EPiServer-CMS/7/Editing/Customizing-the-TinyMCE-Editor/

It's going to be a little more difficult (if not impossible) to remove the epi_ related classes, since the EPiServer TinyMCE editor uses those to style the placeholders for EPi-related item, like the dynamic content and personalization containers.

If you want to see what's loaded into the editor, watch the network traffic via a browser developer tool or Fiddler when you open edit mode for an XhtmlString property, then just look for the CSS files.

All right. I guess that I'll have to skip the styles-dropdown then.

Using the guide I've created a TinyMce-class using TinyMCEPluginNonVisual. It works fine in classic edit mode but the tinymce-editor chrashes when on on-page edit mode. Do I have to create the js-files under util/editor.. etc even though I don't have any javscript code?

My small plugin:

    [TinyMCEPluginNonVisual(
           AlwaysEnabled = true,
           EditorInitConfigurationOptions = @"{
            theme_advanced_blockformats : 'h2,h3,p'}")]
    public class EditorSettings { }

@Alexander: Yes you have to create those files. 

Thank you! Now I've got it to work.

Optionally, you could add an empty file handler or a virtual path to an empty js to deal with the TinyMCE error. Check out this post: http://cjsharp.com/blog/2013/04/15/how-to-add-valid-elements-like-iframes-to-tinymce-in-episerver-7/