Forget the plastic strip. Get yourself a rotating hand auger. Push it into the drain until you feel resistance, rotate the auger until it moves through the bend, repeat until you've cleared it to the main line. Keep the auger close to the drain all the while and have a little water running as you do all this. Pull it out slowly, rotating it and moving it into and out of the drain. The auger costs about 25 bucks but you can use it again and again. It will pay for itself the first time it opens a drain.