Can I install multiple flavours of Linux?

Most distros these days will automatically detect other OSes already installed on the system and provide a multiboot menu for you. I would recommend installing RHEL first, then installing the other two (Edubuntu and Fedora Core) in whatever order floats your boat, as RHEL is probably the least likely to provide automatic setup of a multiboot menu (I haven't touched RHEL in a while and don't recall its install process very well). Make sure that, while installing these OSes, you do not let the install process take over the entire hard drive.

I've assumed that by "Redhat" you mean Red Hat Enterprise Linux (aka "RHEL"). The same caveats apply to old pre-Fedora Red Hat Linux versions, too, though -- least likely to automatically set up a multiboot menu for you, and I haven't used it in a while.