If you have to clean the glassware, then yes, some oxidizing reagent should help. Since you're home, you can even use a 10% household bleach solution. Through rinsing will be important, to get out all oxidizer, soap (which you will need to help clean anything). You might want, after several tap water rinses and distilled water rinses, to rinse a couple of times with acetone.
You're new to chemistry, it seems, and you're a little stuck in the "gee-whiz" phase of Citizen Chemistry. Let me try to say what's on everybody's mind -- you didn't create a brand new, fantastic, space age compound from vinyl tubing, it's platicizers, water, bacteria and household vinegar. I'm finding it tedious to hear everyone keep hinting at that when you offer new opinions regarding this materials physical structure, and source. It's likely a sloughed off layer of plastic or a bacterial biofilm, everyone who's left their condenser going has seen this, and their only response was to ignore it, or go get some fresh tubing.