Hello Freedom Patriot, welcome to the site.
You won't be able to put 4 full size dvd movies onto one dvd and maintain good quality if you intend to keep them in dvd-video format. It is possible to convert them over to Xvid or Divx format and put 4 of them on a double layer dvd and have excellent quality results.
DVDShrink and DVDDecrypter are no longer being updated. I suggest using DVDFab HD Decrypter to rip the dvds to the hard drive. It is the free section of DVDFab and will continue to function even after the trial for the main part of DVDFab expires.
If you are going to compress or convert your dvds, I'd stick with ripping as files. One exception to that is if you want to convert to xvid using Fair Use Wizard....it requires an disk image or unencrypted disk.
If you were simply reducing one movie to fit onto a single layer dvd...approximately 4.3gb, I'd say use DVDShrink or the free version of DVDRebuilder. Since you want to put so many on a disk, you need to convert to xvid or divx, and I'd say look for a target size of about 1.4gb for each movie. This lets you put 3 on a single layer disk, and more on a double layer. (only use Verbatim brand double layer +R disks by the way). You can use AutoGK or Fair Use Wizard or Xvid4PSP to convert to xvid avi.
Burn these xvid or divx videos onto a disk as data. Many newer dvd players can play them, but you'll need to make sure that your player can handle avi files before conversion.
You won't need a menu converting to xvid or divx. Your player will let you select the movie. If you absolutely have to have one, then look into one of the programs made by Pegasys with Divx authoring. TMPGenc Author used to be one, but I'm not sure it is still available.
Now, most of that assumes you have a dvd player that can handle xvid or divx video. So, what if you have to have them as dvd-video? Get less ambitious on the number of dvds you burn to disk. Once you have the original on the hard drive, you can use AVStoDVD, DVDFlick, FAVC or DVDStyler to build a new dvd (with menu) from a couple of your decrypted dvds, but even then I'd use double layer disks to maintain quality.
Double layer disks are much more expensive than regular dvds, and there really is no substitute for Verbatim.