How do I get the oily taste out of my new waterlines?

First, find out the source of "oily" taste in your water. Most likely, there was some work done on your plumbing system, and what you taste is the left-over oil from either threader, or some device installed in your plumbing system. To get rid of it - you have to flush it out by using your plumbing system. It may take few days, but it will eventually go away.

Hope that helps

Milo

You just have to keep flushing it through those new lines, and drink bottled water until the process is finished. Are all the water lines in your house new?