Back in the fall I put 2 coats of Collinite 805 on and it has held up great, however I am thinking of claying and putting another coat on this spring. Do I need to strip the Collinite off before claying? If so, what should I use? Dish detergent?
^ What he said. There's no need to strip -- especially since you are using the same product. If you feel the need to, some so an IPA wipedown after claying. Something like P21S Paintwork Cleanser would also work.
My opinion differs. I believe after a long winter of driving, the old coat of wax (what's left of it) needs to be removed and a fresh one applied.
An application of light polish will take off the remaining wax and clean the paint of crud, grime and dirt that accumulated over the winter. If you don't have a polish handy, try one of those pre-wax cleaners from Mothers or Meguiars.
Once that's done and your paint is freshly polished, apply all the wax you want. The car should look great and ready for good weather driving.