edit: Seeing the screenies, it looks like it's probably a bug or corrupted file or something. If you haven't already, run your patcher, but other than that you might need to reinstall RO (hopefully you still have the installer, but if not, re-download it). You could also try some of the various "RO Cleaners" and things like that the devs have posted, but I am not a dev so I don't know if that will fix your problem or not.
It might be worth trying to mess with your resolution anyways, as it could also be a problem with your video driver, but since they appear in the screenshots too I would doubt that.
Short of that, I'd recommend playing around with the various resolutions of the game; perhaps one fitting the aspect ratio of your monitor would be better, if you're in full screen - or just try playing in windowed mode.
In case you don't know how to do that, go to your RO setup directory which is either C:\Program Files\Gravity\RO or C:\Program Files\Gravity\RO\AnthemRO unless you changed it to something else, and run the program Setup.exe. From that program you can experiment with either using Full Screen Mode or Windowed (that's with the checkbox unchecked); you can also modify the resolution, which will be three numbers separated by "x" such as 640x480x16.
If you're in full screen mode, you should probably use whatever item is at the bottom of the list, that is, the highest resolution, since it's likely to be your native resolution and will therefore provide you with the best aspect ratio (which will prevent sprites from looking "warped" like a square). If you know how aspect ratio works, you could use a calculator to work out the exact ratio of your screen and find non-native resolutions with the same aspect ratio, but otherwise it's probably best to stick with the native resolution. Or you could just run it in windowed mode, which is what I prefer to do, since I frequently multi-task when playing RO and thus have a much easier time if I'm able to Alt-Tab more quickly (since it has to change screen modes when you go to full screen mode).
It's up to you, either way, but I'm guessing if you either change your resolution to the native resolution or else run RO in Windowed mode, that is almost guaranteed to fix your problem (I can't think of anything else that could cause that, except a major bug in the client which is unlikely if nobody else has experienced it).