How do I stress test and/or find out if my network and system are exploitable?

I've set up a few machines running centos for the servers and ubuntu for the desktops. They're all running in VMs. I've tried to secure them as much as possible and now I want to see if they're secure or if there's something I can exploit.

I'm a bit new to the sysadmin part but I'm an average linux desktop user.

tl;dr: wondering how to test the security on my systems and network.