What you need to do is to have all of your project files all in one folder and not scattered from many sources. Then all you have to do is copy that file to whatever system you are working on and you will not have a problem. Vegas may prompt you for the location of files but it will tell you where it recorded the file to be so all you have to do is navigate to that location and select the file. Any other media from that folder will also be found.
Your media is offline most likely because Vegas does not know where to find the source files. If you strive to keep all of your folders in a clear concise format you will save yourself a lot of headaches later on. You can always use the Save media with project option but all that does is copy all of your media into one location and you will lose any folder structure you may have. It is not a good function to use. Hope this helps.