The best thing you can do is have a known clean copy of your site that you can compare the server's files against. Most hacked webservers that serve virus infections come from changing the content of scripting files that server is offering to clients. Look for files with different checksums or new files.
There are also cases with forums type sites where the infection will come through XSS. In an effort to hide infections from site owners, sometimes infections are only served up if the visitor has a referrer tag from a search engine in their request.
You can also run 3rd party scanners against your website. http://www.antihacksecurity.com/scan-a-website-for-virus-malware lists some of those options.
Since you're talking about your machines connected to the same server, I'm assuming you mean a LAN environment where that server also offers file sharing. Among other things, it's often very good practice to split servers that offer external facing services from those offering internal facing services. Further, that poses the idea that the server may have been compromised and then used as a launching point to infect your machines.
Identifying the particular infection will also allow you to research the most common way that it is transmitted. Most virus packages are full packages that an attacker can drop & move on. That means they'll behave the same way.
Ultimately, verification breaks down into two possible areas: scan try to find "bad stuff" or authoritatively certify that everything on your server is "good stuff." The second one is more secure, but requires the right type of environment and planning.