The way I make my multi strand seed bead necklaces is to take a piece of wire (I use 20g.) and make a loop in one end.

Then I tie all my strands to it. You can be as messy as you like since it will be hidden by the cone. ;)  Just make sure that your knots are secure.

Do the other end of the strands the same way.

Now slide the cone down tight over the strands and make a wrapped loop in the end of the wire.  
Now you can either finish the wrap and add your clasp by using jumprings like this......
Or you can add your clasp to the wrapped loop before you finish wrapping it.

For this one, I made my own hook, and just made the loop on the other side larger.
Either way, if you are going to be adding a cuff to your necklace, make sure that the clasp is small enough to fit through the cuff so it can be easily removed. :)
Making a multi-strand necklace
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If you don't have any cones on hand, it's fun and easy to make your own. This one was made by using about 6 rows of tubular netting. You can find the instructions here.
Or try using any tubular stitch....peyote, R.A.W., etc.  It's nice to learn to do these because then you will always have the right size cone on hand. :)