There is no reason to expect a USB CD-ROM drive to behave any differently. The problem is happening even using imgmount in DOSBox and accordingly is completely independent of your CD-ROM hardware. As Dominus suggested, "something is not right with your machine it seems".
Like I said before, you might want to consider booting Linux on your system – strictly as a test. You can download a "live" distribution that will boot from a USB drive or from a DVD-ROM without affecting your Windows installation or anything else on your hard drive - even something like the Linux Mint installation disc will do. Generally it will autodetect all your hardware and network settings and you can install DOSBox just by typing "sudo apt-get install dosbox" at a command prompt. (The only catch is that you'll have to do that every time you start your computer from the USB drive or DVD-ROM, unless you set up persistent storage, which is probably more trouble than it is worth.)
If CD music sounds normal in Linux, then you can be sure that neither DOSBox nor your CDs are the problem – and you can start looking for what might be wrong with your Windows installation.