I think you have to do something like the following:
1) create a native DLL that exports:
"HookCompleteInjection" (in case of 64-bit) and
"_HookCompleteInjection@4" (in case of 32-bit).
The expected entry point signature is REMOTE_ENTRY_POINT (see easyhook.h and RemoteHook\thread.c)
2) make a call like this from your host C# process:
NativeAPI.RhInjectLibrary(process.Id, 0, 0, "TestDLL.dll", "TestDLL.dll", IntPtr.Zero, 0);
Note: EasyHook is not designed to inject any old DLL, it is designed to inject DLL's made specifically for use with EasyHook (i.e. one that has the HookCompleteInjection export).