Ok, what kind of Medela pump is it? The Pump in Style (double electric that usually comes in a black carry bag or backpack), the Mini Electric (small yellow model that usually only pumps one breast but some models will double pump) or the Harmony (manual single pump) are all single user pumps designed to be used only by one person. The Lactina (big, blue hospital grade common as a rental), and the Classic (rarely leaves the hospital) are designed to be used by multiple users who each buy their own kit--breast shields, bottles, valves, tubing, piston assembly.
Gardenmommy is right, sharing of single user breastpumps is not recommended. Even after boiling yeast and some resistant strains of staph or other bacteria can remain in the plastic. That said, many of us do share pumps and parts without problems. Most of the diseases that are mentioned in the breastpump sharing warnings are body fluid born and not likely to survive a long time on a pump--AIDS, hepatitis, Cytomeglavirus.
The electric single user pumps--PIS and Mini Electric--I would only share with someone I knew very well and trusted. Someone I trusted enough to breastfeed my baby. Even though you may not be able to see it, milk solids can get into the motors of those pumps and contaminate milk across users. I have shared a Harmony and an Avent Isis because they can be fully disassmbled and sanitized, but I don't know if I would do it again. I am more cautious now that I know yeast and staph can lurk in the plastic even after sanitzing. Since it's clear that your friend isn't clean and didn't take care of the pump, I'd be even more cautious about sharing with her. In your situation, I think I'd ask her to replace the pump. Even if she won't, I'd probably discard the pump in its entirety. If I were only going to be pumping occasionally, I'd buy a Medela Harmony manual (about $40) and consider my money well spent for the peace of mind.
All that said, to answer your original question, the best way to get the stuff off is probably to wash the parts by hand in the hottest water you can stand with dish detergent and a whopping dose of white vinegar. Let everything soak for a bit then use a bottle brush and rinse well.
Then soak everything in a 1/2 vinegar 1/2 water solution to sanitize it.
If the pump has tubing after washing and soaking, you take the tubing outside and swing it around your head really, really fast like you're about to throw a lasso and that will help get most of the moisture out of the tubes then hang them to dry or connect them to the pump and turn the pump on until they are dry.