I just picked up a Bodnick Slick Stick. It has the original whisper string on it. It is extremely small I believe 10 strands. I have Beman Centershot arrows and the nocks just fall off the string. If I went to a larger string say 12, 14, or even 16 strand what differences would I see in a larger strand string as far as nock fit and performance

I think you would be better off re-serving it, either with thicker serving or two layers of serving.  You kind of have to experiment with .019, .021, .024, etc to see what works best.  Personally, I would rather use two layers of thin serving than one layer of .030, but that might just be me.  If you use two layers of different diameter serving, put the thinner layer on the bottom.

However, if your nocks are REALLY loose, you might be able to put a layer of thin serving on top of what is already there.  It's not really the best way to do it, as the thin serving might sink into the thicker serving below, but it might work, and would save you the trouble of removing the original serving.

I run 12 strand strings and they work great for the center shot an BE vintage nocks.

Try a few wraps of dental floss just around the nock area on the serving. Rod Jenkins suggested it and I've tried it. Works well.

McDave x2 --- learning to serve is a good thing and you'll always be able to get good nock fit.  I also have used dental floss in a pinch--- it works just fine.

You could just serve the nock area.Does not require much skill.I use nylon thread or braided fishing line in lower poundage like 10- 15# test and the dental floss mentioned above is used by guys as well.I use a little super glue to hold the threads together and a lighter to singe any thead sticking out

All good advice here.  I make my own strings with 10 strands, and have no creep after break in.  Serve .019 under the bow square, then finish with .024 for a very nice nock fit.  Nock fit is something I'm picky about too!  The dental floss suggestion is also going to work, just don't over tighten your knot, as you don't want the floss to cut through the serving. 

Best regards, Chase