The DllNotFoundException is caused by screwed up assembly dependencies when the dll package was built. Nuget installer for AutoitX is not working for the same reason (more details here). Bottom line - Visual Studio doesn't know it needs to copy AutoItX3.dll to the output directory. It only copies AutoItX3.Assembly.dll, and forgets about the other one.
The easiest solution is ensuring AutoItX3.dll is in your output bin/Debug or bin/Release directory, when you run your program (basically the same directory as your exe). You can do that by simply placing AutoItX3.dll in the root of your project in visual studio, and then setting its properties to:
Copy to Output Directory: 'Copy if newer'
