I have my website, I need to check browser compatibility of my website across all browser and OS combinations. Sp Is there any other way to test websites on different operating systems instead of setting up a new OS machine?
Why would you run your website on different OS? You need to test all combinations of browser/OS for CLIENTS. Your server stays where it is.
If you need to change underlying OS for server, it is completely different ballgame, sysadmins would know how to do that.
There are plenty of simulators for various kinds of OSs and browsers. I just searched for "Win XP emulator online" and found this: http://virtualdesktop.org/complete/xpsp2/index.html. The question is whether it is accurate. You would need some research to form your list of reliable emulators.
Besides, public cloud vendors (Amazon, first of all) usually allow creating free virtual machines in their clouds for a trial period. You should check what options you can find there. Of course, they will not provide you a wide range of versions, but still worth checking.