I was testing the plugins and adding stuff to my first project, but apparently, I could not hear any component included with Sonar.
 
No sound from the VST plugins, no sound from the audio or MIDI tracks when I played the project. Just nothing!
 
I do not know if I am missing an additional audio interface or device, but this issue does not motivate me to continue on with my first project. I seriously need a little bit of some assistance here.

Before anyone can help you, you need to explain what you're doing and what equipment you're using, and it would be helpful for you to look here:
https://www.cakewalk.com/Documentation?product=SONAR&language=3&help=Welcome.html

Yep, as Larry said, the first thing we need to help someone is a bit of a list with things like
OS and version
Which version of Sonar
Audio interface ( yes you do need one for recording audio) 
Computer basic specs like i7 16 GB RAm etc. 
 
You cannot expect to use any DAW without worKing your way through the documentation, tutorials and video's
 Start simple and record a easy song with drums and a guitar and vocals. If you play keyboards bonus you have a huge pallet of sounds to use. We are all happily recording stuff and you can too, just take a deep breath, relax and start learning..It took me 10 years before I actually knew what I was doing and at this point I still only understand 3/4 of what Sonar can do,,

I agree with Larry and Johnny's advise, you need to give more info.
Sounds like your audio device is either not hooked up or no not recognized when opening Sonar .
This will also help you get set up.
Enter your device name and Sonar version and it will give detailed instructions on set up.

I use SONAR Professional. The audio interface I use is the ASIO4ALL, but apparently, there is another interface known as FL Studio ASIO in which I, for some reason, cannot select in my preferences.
 
My computer, running Windows 8.1, uses a total of eight gigabytes of installed memory, and it is a 64-bit PC, but apparently, the version of SONAR Professional I have only runs the 32-bit version. There is no 64-bit version.

OK first When you install Sonar Professional it askes you durring the install to choose 32 or 64 bit. You just might not have been paying attention. You really should re install it because working in 32 bit is a bad idea in this day and age. 
 
ALso you need to go into preferances and set you audio setting so that Asio4all is your audo device. 
Asio4all is a good driver for on board I use it on a laptop I have for working on midi projects. You cannot record audio with that system without issues so if audio is in your plans then start shopping. 
 
Go through the Documentation on how to set Sonar up to use VST's,, I'm not about to typoe out the same information here, it is already nicley excplaind in the help and documentation files. 
You can use Google to ask questions. 
https://www.cakewalk.com/Documentation?product=SONAR%20X3&language=3&help=SoftSynths.01.html
 
 

I already have ASIO4ALL as my default device for Sonar.

To put it simply.

A sound card or sound device is one of two things, either :

@ a physical device - ie something you plug into a USB or Firewire socket on your PC.
@ Or a device that is built in to your motherboard.

Which one do you have/are you using ?

Next step :

99/100 of times the former will have its own proprietry drivers, the latter will need Asio4All. If you have the former, what is it ?

What people are trying to find out is which of the two do you have ?

Cheers,
Jerry

I'm guessing Julie Zhu is using the onboard sound device. Somebody smarter than I am can confirm this, but doesn't SONAR have a mode called WASAPI recommended for use with onboard sound? I've never needed it so don't know anything about it.

In any case, Julie, I think you will be happier in the long run if you can get yourself an external audio device and use its proprietary ASIO driver. They start at less than a hundred dollars. If you don't want to or can't, let this forum know what you are using and we'll go from there. But read the links folks have given you (above) to get started.