How to attach steel cable to threaded rod
Most of the attachment methods I can think of will require making a loop in the cable to go through or around something.  There are crimp-on clamps that are basically a metal tube, but you need a heavy-duty crimping tool.  There are clamping U bolts, that only need a wrench, but they are ugly honking things to leave visible.  

This type of clamp is pretty streamlined and doesn't need special tools (it comes in various sizes for the cable):



Since you need a loop, anyway, you could skip a separate cable clamp to pass it through for attachment to the rod.  Just loop the cable around the rod, and use a nut on each side to keep it positioned where you want it.
Actually, you can clamp a steel cable loop together without a hardware clamp.  Make the loop and bind it together by winding a piece of wire around the two a bunch of times.  Then cover the "clamp" with heat shrink tubing, making sure you enclose the cut end of the cable.  It won't be nearly as strong as a hardware clamp, but it will hold well enough for "decorative" purposes.
You mention an approach where you just pass the end of the cable through a hole.  You would still need to deal with the end of the cable to secure it and keep it from unraveling (and protect yourself from stab wounds; the ends are sharp).  

If there won't be any stress on the cable, you might be able to use a really large crimp-on loop-type electrical terminal.  Steel cable doesn't compress like copper wire, so you would need a heavy-duty crimper.  The terminal would go on the end of the cable and the threaded rod would go through it.  Again, you could position it on the rod with a nut on each side.
Another approach: this would be similar to the old binding posts used for speaker connections.  If the threaded rod is a much bigger diameter than the cable (on the order of three or four times or more), drill a clearance hole through the rod at the cable locations.  Pre-position nuts above and below the hole.  Pass the cable through the hole and bind the end with something like heat shrink tubing.  Then tighten the nuts against the cable to lock it in place.  You might get away with a nut on just one side, but tightening it against the cable might sheer the cable.