I had tried vinegar but it left a flavor even after rinsing. I had better luck with a baking soda soak for removing flavor/odor, but that doesn't actually clean the wicks, etc. So I ended up doing dish soap, well rinsed followed by a soda soak.
I had also heard that denture cleaner works, and am experimenting with that. So far it works very well, but what I had available was mint flavored and left some flavor. Okay with my menthol and spearmint juices, not so good with tea or fruit. So I am going to order some unflavored denture cleaner and try that.
All of the above require a rinse, of course.