Relay for electric oil filled heaters - does it have to be so noisy?
No, not all relays are that noisy.  Indeed, a solid state relay will make no noise whatsoever.  For example, the Honeywell rt850t-240 is an example of a heater control relay that is silent.  You can read about that here:  http://bit.ly/1Caf1np

NOTE: I do not claim that this relay will work for your particular application.  This is just an example.  However, I believe you should be able to find something similar that will be completely silent.

To answer your other question, a relay is required because standard thermostats run on 24V, and the heaters are either 120 or 240 (actually, there are a number of other good reasons why you'd want to use a relay instead of having the thermostat switch the load directly, but that's the easiest to communicate).  The Honeywell relay I linked to above connects to a standard 24V thermostat and will switch a relatively large 240V load.