Oil in coolant

2001 Passat. Check engine light came on. Autozone's free check found an O2 sensor went bad. Upon having that fixed, my mechanic-friend noticed oil residue in my coolant tank. I have since heard a few theories about the root of it: the head gasket, a seal broken on a washer, and the oil cooler. My actual mechanic believes the oil cooler to be the problem. Who is right? And should I get a new reservoir and hoses put in, like someone else I know, or would that not really help at all?