How to start streaming

You say you have “ a large collection of such files on my PC and external hard drives which I have converted to CD”. I guess I confused as to what that means?
jond is correct, you need a device that can stream. There are dedicated streamers by many audio companies now and you can use a computer as well. One thing to keep in mind, if you are using your new DAC as an alternative DAC to the one in your CD player and wish to use it also with a streaming device, you will need a device to switch it, like a preamp or coax/usb or optical switcher.
Perhaps some here, who use an external DAC with both a computer and CD player can offer advice if you are using a CD player.

USB from computer to DAC would be cheapest and easiest way. 

Or there are many wireless audio or media streaming devices that could be used.  Just pick one.  

Plex is a very good multimedia streaming software system that runs on most any device and supports CD resolution digital streaming of music files.   Look it up. Server and web site client is free.  Apps for Smartphone or tablet are just a few bucks.  Need to be a little computer savy to set it up though perhaps.  

2psyop:  I have downloaded many, many files for the purpose of creating CDs of them to play on my system.
Just the opposite of converting CDs to files.

@rvpiano,

What is the resolution of your stored files? If you own a iPhone/iPad I would recommend Apple AirPort Express and a 3.5mm/ optical cable setup.

https://www.apple.com/airport-express/

https://www.amazon.com/FosPower-Toslink-Digital-Connectors-Strain-Relief/dp/B00T8HWUVS/ref=sr_1_1?ie...

If your files are at least cd quality (16bit/44.1khz) resolution or higher then you should look into a dedicated streamer like Bluesound Node,

http://www.bluesound.com/en-us/products/node-2/?cl

You can use digital coax or Toslink cable from Node to Gungnir DAC. Or use RCA out from Node to your preamp/processor to bypass Gungnir DAC. Just connect your NAS drive to Node via USB cable and start listening to your stored files. I believe Node comes with all the cables you would need and their customer service is top notch.

The Node setup is very easy, will yield better sound over PC and offers many options to stream music like Tidal, Spotify (with paid subscription).

Hope this helps!