Can a strange-smelling odor be secreted from my cat's skin?

My cat is ten years old and I noticed that some pillows that he slept on smelled terrible! But the strange thing is that he doesn't smell bad---it's just things that he sleeps on, or if he's in a room for a long time. Could he be secreting an oil of some kind? Also, he's very skinny, even though I feed him a lot. Is he okay?