Danno is correct. It's a freewheel as shown by the 2 removal slots. Using chain whips will remove the cogs, but the body will still be there ... not what you want.
The only question is if you really need to remove it. Some "wobble" is normal with freewheels ... no big deal. A bit of looseness is also no big deal. Do you have a real need to remove it ? If so, get the correct tool and use the correct method of using the QR skewer to keep the tool in place so it won't slip off like it did last time.
If you decide to leave it on, you can dripple a teaspoon of light oil (10w-30) into the bearings. Spin it slowly backwards and dribble the oil between the fixed body & the moving cogs.
Last edited by Homebrew01; 10-26-10 at 04:41 AM.