The source code is readily available for the Enterprise Library so if you are going to use it, you should rebuild it using one of your keys so that it can be put in the GAC and then easily reused by other applications. Once that is signed, you should do the same with your web parts.
However, if you wish to DLLs without strong names then you will need to place all of them in the /bin/ or /_app_bin/ folders of the web application in question. You may also see security restrictions as a result of this. Also, if you have multiple web applications then you will need to copy them to place them in the proper folders for all web apps that will need them. You can see how this could easily become a significant maintenance and troubleshooting issue.