Are you using only program mode? Have you inadvertently set the mode dial incorrectly? Are you letting the camera "pre-focus" before you snap the shot? If you just frame the picture and mash down the shutter button, even the FZ20 takeshalf a second to capture the image, and if you move your hands during that time, it will blur the images. Try pressing the shutter halfway till you get the focus grid and the little round focus indicator above itlit up in green, then snap the shot and see what happens. That does two things: it gives the camera time to focus on the subject you're shooting, and also dramatically reduces shutter lag time to almost nothing.
OIS modes - mode 1 leaves the image stabilizer on all the time, but it doesn't work as well for removing the jitters. In mode 2, the camera only turns on OIS when you press the shutter, so it stabilizes the lens at the exact instant you take the picture, and supposedly gives better results.
You mentioned "holding the camera still and use the 2-second timer". Are you using the timer hand-held? If so, why? Trying to hold the camera perfectly still for that long is just asking for trouble... the only time you should use the timer is if you have the camera on a tripod or other support that is immobile.
The FZ20 is capable of marvelous clarity, indoors or out. A look at some of the shots posted on this board should convince you of that. Take some time to read the manual thoroughly and make sure you understand how to use the camera for the kinds of shots you want to take. If you do that and it STILL doesn't give you clear pictures, then consider taking the camera in to have it checked out.