Hi. Yes, it is possible to compress many gigabytes into a few megabytes or even less without data loss, but that will hugely depend on what kind of data you have. Some types of data are basically incompressible, while other types can be compressed quite well by tools made to work specifically with those contents. An example is trying to compress a WAV file with 7-Zip versus compressing it with FLAC or another lossless audio format, which will generate a substantially smaller file with no quality or data loss. Another example is compressing BMP files into PNG, which again can generate lossless compression much more effectively than using general-purpose compressors such as ZIP.
The problem is that you probably won't have WAV or BMP files around, and that the bulk of your files is basically incompressible (or too little compressible to be worth the effort), most likely due to already being in compressed formats.
So you only have three options: 1) using lossy compression for images, audio and videos; 2) getting rid of some of the data; or 3) getting a new hard drive or at least a few DVDs where you can offload some of the data.
