Package contains EditorOnly data which is not supported by the current build

I found a solution for the ServerDevelopment build. It’s all about cooking the content for the server. Some other posts may talk about using the Cook command in the editor, but you need a separate cooking operation for the server. If not, I believe it will rely of whatever is available to pack and some assets will be incompatible.

They are two way to do this: You can use Unreal Front End to specify a server build for your project with cooking included (If you built your engine from source, you may need to compile UFE yourself as a Visual Studio project in the engine tree).
The second way is using the command-line (this is my favourite way of doing it).
Check out A new, community-hosted Unreal Engine Wiki - Announcements - Unreal Engine Forums and run either “Compiling the dedicated server (With PAK files)” or “Cooking the dedicated server (With PAK files)” script. Make sure RunUAT is part of your path or surround the complete path to RunUAT with double quotes. The latter is to avoid the engine path to be prefixed to your project path (a bug in UBT that took me a while to understand).

As a side note, I would encourage you to get familiar with this wiki. The power of the command line to cook and build greatly increased my productivity as I can now dedicate a build script for nightly builds.