A set of software products differ only by their resource strings, binary resources, and by the strings / graphics / product keys used by their Visual Studio Setup projects.
You can add conditionals to elements within the MSBuild file. So for instance, if you have "Debug" resources and "Release" resources, you can place these within two separate folders (e.g. Debug and Release). Then, within your MSBuild file you might have:
True
True
Resource1.resx
True
True
Resource1.resx
ResXFileCodeGenerator
Resource1.Designer.cs
Resources
ResXFileCodeGenerator
Resource1.Designer.cs
Resources
Provided all of your access to your resources are via the Resources.Resource1 class, then you get two different sets of resources for debug and release builds. Obviously, this can be extended to further configurations.
Unfortunately, I don't think you can force the resources to use the same baseName (as provided to ResourceManager constructor), since it's based on the path within the project, and I can't find a way to override that. If you do need them to use the same name (if you're manually creating ResourceManagers, for example), then I'd suggest having a Resources1.resx (plus associated cs file) at the top level of the project, and not under source control. As a pre-build event, copy the required .resx file out from the Debug or Release directory as appropriate. (In this situation, you'd probably want to force it to not compile the .Designer.cs files within the subdirectories.
Edit
Forgot to mention (though it's seen in the above excerpt from the MSBuild file) that you have to set the Custom Tool Namespace on each .resx file to the same value (e.g. Resources), otherwise it also defaults to including the folder name.
Edit 2
In response to query about checking that each resource file contains the same resources - If you're using the Resource class (e.g. Resources.Resource1.MyFirstStringResource) to access your resources, then switching configurations will result in build errors if the required resource doesn't exist, so you'll find that quite quickly.
For the truly paranoid (i.e. if your build process takes 3 days to build all configurations, or something equally mad), at the end of the day, .resx files are just XML files - you just need something to check that each .resx file with the same filename contains the same number of elements, with the same name attributes.