I have a Radeon HD 6970 and wanting to do EyeFinity. My question is am I able to do a 22 Inch monitor in the middle and two the same 19 inch monitors on the outside with different screen resolutions? (Middle 1920, 1080 and side two are 1280, 1024) Will it not work?
Well, it should work but it won't be pretty. Eyefinity will default each of your monitors to the resolution of the lowest monitor's maximum resolution. This means that all three of your monitors will be told to display @1280x1024.
Since that is a fullscreen resolution my guess is that the middle monitor (being a widescreen) will have black borders on its right and left side. It'll either make black borders or stretch the 1280x1024 image to 1920x1080. 1280x1024 stretched to 1920x1080 isn't going to look good at all. Either way, your 1080p monitor won't look ideal under that resolution.
Outside of games, you can certainly use multiple monitors to extend the desktop. Windows is fine with mixing resolutions and will still output to them in their native resolution. But with eyefinity a single surface is created that must be constructed of blocks of matching resolutions. That is why your 1080p monitor will be forced to run at 1280x1024 in eyefinity gaming. Hope that helps.