Audio Data Folders

So when I moved to Sonar X3 Producer, I simply dragged each song's audio data into sub-directories. D:/Sonar Projects/Song Name/audio

You need to drag the exported audio into a sonar project and then save it. Making sure you enabled CWP with per project audio in your preferences.. You cannot transfer audio files from one program to another like that. That is not how it works.
 
Cj

You did the right thing to start with but you forgot to then go into preferences and change your pathways to the folders you want to use. Sonar has a default file system but nobody with any sense works that way. Most of us change the file storage to our own custom set up. 
 
The most bullet proof method:  If you use SAVE AS and check copy all audio data with project then everything will be put in the folder you browse to to save it. 
Most of us use the Per Project Audio folder option. But really, There are many ways that will keep your songs in the same folder if you take the time to set it up the way you want it. Sonar gives you lots of options. It's just the default system is not the best for most people. 
 
Faced with your situation what I would have done is to ( outside of Sonar) create a new global folder to hold all these projects on my Audio Data drive. 
I have Sonars Project path default set to open at the root of my Audio drive. The Audio drive has a folder for each "album" and a template folder. 
Inside that folder create a new folder for each song. 
Now copy the audio folder for that song from the other software and name it " Vegas Audio" 
Do this for each song. 
Now open a Sonar Template you created for this from you templates folder. 
Before you do anything perform a "save as" and browse to the song folder you just created. 
Name the Song and save it. Make sure to check the copy Audio' box. 
Now you can use the media browser to drag and drop the audio as you need it to this project. From now on a SAVE will keep the audio with the project. Your original Vegas audio will be a copy to use as a back up.  
This is just one way to make a bullet proof working copy of a project. 
I even save a MIDI version and make sure these are also backed up to other hard drives as well, Use dates when creating folder etc.