Comparing the ultra-wide, crop-sensor camera lenses is an extremely difficult task, so I’ll put the summary first: they all deliver excellent image quality, and you can’t go wrong with any of them. To my ‘just taking pictures’ assessment, they are all excellent. There are some differences though, so I’ll try to point those out so you have a better chance at choosing the one that’s best for you.
The Olympus 7-14 f/4 is the widest zoom made, and probably the best wide zoom available in 4/3. It has virtually no geometric distortion, little vignetting, and is sharp in the corners throughout its focal range even wide open. There’s a bit of chromatic aberration in the extreme corners at wide angle, but that’s about the only flaw (other than the price) one can find.
The Olympus 11-22 f/2.8-3.5 has little distortion, excellent flare control, and very little chromatic aberration. It has decent image quality wide open, but sharpens noticeably when stopped down one stop to f/4-5.6. A very good lens.
The Olympus 9-18 f/4-5.6 is a very small lens, which is important if it’s “in the bag just in case I need a wide angle”. Like the other Olympus lenses, it has very little distortion and is nice and sharp even wide open. Of course, that’s more important since it doesn’t have the wide aperture of its Olympus cousins. Overall its excellent value and a very decent lens for the money.
The Sigma 10-20 f/4-5.6 has a bit larger range and provides excellent image quality, although it has a bit of barrel distortion at the wide end. It’s quite sharp in the center even wide open, a bit less so in the edges until f/5.6 or f/8. It’s internally focusing, so if you plan on using a circular polarizer (not always the best idea on an ultra-wide).

But like I said above: they’re all excellent. We hardly ever get anything but happy comments about any of them.