Elliemare
I am a massage therapist with over 14 years experience. I've never heard anyone ever describe someone's muscles as "oily inside"? That's just odd and certainly not a clinical description of what she was feeling.
I wouldn't put too much thought into it. Everyone has unique musculature, no one person's muscle tone or the "feel" of their muscle fibers is exactly the same.
Of course there are abnormalities within muscle tissue like triggerpoints or adhesion, but as for the over all feel of the body of the muscle, each person is unique. Some people have naturally very rigid muscles, others very soft. Perhaps your fascia is very loose and viscous and slides easily? If so, that is a good thing! A very good thing!
I wouldn't worry too much about your oily muscles! I'm sure your just fine.