If your site always looks wrong in Internet explorer, no matter which theme, then odds on you have copied some Word document formatting and pasted it into Moodle. Copying and pasting Microsoft WORD document text is one of the biggest problems faced by course creators. It is so bad that in some schools it is banned!
The problem stems from the fact that ever electronic WORD document carries with it the formatting code it uses to make it looks correct on the page. This 'formatting code' is what screws up your Moodle site in IE, because IE reads it and responds to it.
What you need to do is check that any text you added to the centre column on any course page including the frontpage is free of this formatting. The best way to check is go into Edit the section you last added and text to and look at is using the HTML viewer in the text editor menu. It's next to the ABC spell checker.
To clean the text up there is another icon in the Editor menu that allows you to strip the formatting from WORD document text. The icon looks like a yellow folder with the letter W in the corner. Hovering over this icon it says 'Paste from Word'. Other icons near this one can "Cleanup messy code"; "Remove formatting"; "Paste as Plain Text", these are all useful but the Word one is the one you need to use, if this is the cause of your imediate problem.
Another possibility is that you may have an out of date Plugin like a Course Format. One that comes to mind is Collapsed Topics by Gareth Bernard. This along with a few others had a bug hidden in it that cause Moodle Themes to break in IE9
Hope this helps?