Stripped screws on laptop?

I'm considering upgrading the memory on my Lenovo G560 laptop. But it seems like 5 of the 7 screws I need to unscrew to access the memory are stripped.

The screws start to come up, but then go around in a circle and I hear a clicking noise with my screwdriver. That's where it ends.

What are my options? I'd be a little nervous about drilling.

Have you considered the possibility that the screw is connected to whatever part it is and is not meant to be removed? I've also opened a laptop only to find that sort of thing.

Try unscrewing all necessary screws and just removing the part.

I agree with Tien.
But if the screws are effeminately stripped, try to pull the screws out while turning with the screw driver.
Lift up the screw head with a pointy tweezers, or a razor blade.
Put upward pressure while turning the screw.

Normally you'll hear that "noise" when the screw is fully disengaged from the laptop body. What you need to do is put a small flat screwdriver under one edge and lift. It may take some force but the panels are made to be flexible and will withstand this. Normally there are little tabs that hold the panel in place even once the screws are disengaged. Lift a corner and then continue to pry along the edge with your fingers from that lifted corner. The panel will snap free. I haven't seen a laptop yet that doesn't have this retention convention. You just have to get a little physical with it.