Hi there Max and Welcome to the Q&A Board!
You mentioned that you've read reviews of these cameras. Terrific! That's a great way to start your comparison.
Though I can't recommend a specific camera I can point out a few of the differences I noticed between these three models that might help in your decision-making process. Since I'm not sure what kind of photography you are primarily interested in or what your level of experience may be, I've selected a few things that I hope will help you. I'm basing my opinions on reviews I've read at a website called "Steves Digicams" (a product tester/reviewer with much experience). Ok, here we go:

As for lens quality, Zeiss is nice.

The Sony showed little noise and practically no chromatic aberration (color fringing). Likewise the Olympus showed no chromatic aberration.
All three cameras produced saturated color with the Canon reproducing color perhaps a tad more accurately IMHO.
All three models have some lens distortion (barrel and/or pincushioning) which is not uncommon in this class so don't fret it too much.
If your interests include macro photography, then the Canon may be the way to go. It allows you to get as close as 1.6 inches near your subject. Yes, the Olympus has a super macro mode which lets you get closer but at that nearness its flash locks out and the tripod mount (you'd want to use a tripod) is made of plastic (could break).
The Olympus, with its 5x Optical Zoom, has the 35mm equivalent of a 38-190mm lens. If you're interested in telephoto photography, the 190mm end would serve you well.
Conversely, if you're more interested in taking wide-angle shots and panoramics, then the Canon with its 28-100mm equivalent lens would be more suitable for this purpose.
Personally, I love Manual mode and all those adjustable/customizable features (like white balance, metering options, etc.)! Some folks are freaked out by them but if you think you'll be inclined to enjoy learning about and using them, then take a look at the Canon.
As for buffering, important if you're shooting a lot of action shots (or in my case, wildlife), the Canon's specs looked good but its lag time was a bit slower than the others if you aren't already pre-focused.
Now that I've probably confused you even more, fear not. All three of these cameras are good, high-end small point-n-shoot models. Being 7 mega-pixel cameras, they all have the capacity to produce (uncropped) photographic quality images at a whopping size of 13x19.

If you're new to photography, all three have plenty of presets. If you're more experienced, all three allow for customizing and manual choices.