I've got a little bit of a problem. I moved into the house about 5 years ago and haven't really noticed this issue up until now, so basically:

I've traced the smell that comes from the sink's overflow cannel. The water never exits the overflow because the holes in the drain are sealed with some sort of clay!? I think this was left from the previous owners of the house. OMG!! What can this be ? What are the possibilities/explanations for this ? I want to try to unseal the holes, but I'm thinking maybe it's something important ? But I hate the water always standing in the overflow and stinking!!

PLEASE HELP ! WHAT SHOULD I DO??

Sounds like they over did the plumbers putty. First just try to poke through the putty with a coat hanger. If you can't open it then removal and reinstall correctly. YouTube - Electrical & Plumbing Repairs : How to Replace a Sink Drain

Sounds like excess plumbers putty from when they installed the drain. If you are lucky, you can carefully probe with a single piece of 12 or 14 AWG wire down to the drain and hopefully push open a hole through the putty into the drain. Do this many times. If this fails, you will need to remove the drain, clean out the overflow and reassemble. You can also try removing some of the water with a straw or tip of a rag and put some bleach into the overflow, it should reduce the smell by killing the bacteria.