I make lots and lots of multi-strand necklaces with nylon cord and glass beads. This is one of the products that I wholesale in large quantities, so it was in my best interest to develop a surefire method of finishing these necklaces.
There are several brands of strong nylon cord on the market. My favorite by far is C-Lon, which I purchase from Marion Jewels in Fiber. My local bead store carries it too, but Marion stocks the entire range of colors, which is astounding.
After you've strung your beads, align your cords and tie an overhand knot with all 3 (or however many you have) strands. Tighten this knot.
Tie a second overhand knot directly over the first one. Before tightening this knot, insert a 2 1/2" - 3" length of wire (I use 22 ga sterling silver) through it. Pull this knot tight, incorporating the wire.
Bend the wire around the double knot and make a wrapped loop.
Add a very generous amount of glue (Hypo Cement is my glue of choice) all over and around this knot. Be sure to get some glue on the wire as well. Don't worry about how this looks -- it will all be hidden from view. Trim the excess cord to about 3/8". Don't forget to clean the glue off your trimmers or your scissors!
Before the glue on the cord is completely dry, insert the wire into a cone end. I use 1/2" sterling silver cones. Be sure to get the entire knot and the loose cord ends into the cone. If necessary, push the loose ends in with a toothpick or wooden skewer, or whatever is handy!
Make a wrapped loop at the very top of the cone. Repeat this process on the other end of the necklace.
Add your clasp of choice and your necklace is ready to be worn.