Is there a stereo system that will record my vinyl records and cassette tapes onto CDs?

You can purchase one of these.
It is pretty easy with the right equipment.

this is better if you don’t want to use a computer…..its a stand alone system that can transfer any audio tape or record directly to CD and can also play them (stereo).

http://www.amazon.com/Crosley-Director-CD-Recorder/dp/B001NLAK82/ref=pd_sim_sbs_e_4

many of these look the same but have different price points, however read the descriptions, the lower priced ones only feature a CD Player not Recorder. This is the recorder.

I have both the Ion and Crosley and both work pretty well.

You are probably better off recording them to your computer using something like Audacity then you can go and chop up your recordings into their individual tracks before burning to CD