Editing resource files without recompiling ASP.NET application
Solution 1:
You can achieve this, and I just did it.
Select the resource file in your project. Change the Build Action to content. Make sure that the Copy to Output Directory setting is turned OFF. When you deploy your project, the App_GlobalResources directory and your .resx file will get copied to the root of your web site. You can modify the .resx file and your live site will recognize the changes.
Solution 2:
A Web Application project is different than a Web Site project. I doubt you can achieve what you want with a Web Application project. You might check out this post:
ASP.NET Web Site or ASP.NET Web Application?
Resources are generally meant to be static. They are items such as images, strings, and files that your program consumes and can rely on being present, (and therefore can be strongly typed in the case of strings/RESX files). The reason for using resources is simply to bundle them in with your DLL's so that distribution and referencing the resources becomes much easier.
Editable at runtime suggests you might want to use project or user Settings, or maybe a database? If you need to use RESX files you might need to write code to read/write them.