Merge Clips in iMovie or iDVD

This specific "Merge" option is for the merging of content which was previously split by the "Split" option. If you place two clips in the same project next to each other the are automatically "merged" together when the project is shared/exported. If the scene change is too abrupt in nature, you can always add a transition effect.

There are only 3 different subjects on that tape (birthday, park, home), so I would like to merge those 18 clips and create only 3 clips to use in iDVD to burn a DVD with.

You have two primary options here:
1) You can create three separate projects and share/export each as a separate clip or
2) You can create a single project, chapter it in GarageBand, and then send it on to iDVD, where, if you have not changed the default settings, a separate sub-menu will be created automatically.
The main difference here will be how the media will be viewed. In the first case, each project clip is considered a separate movie, can be selected independently, and will, after being seen, return directly to the main menu so you can select a different clip. In the second approach, all three clips are considered part of the same movie, and, while each chapter can be entered independently, play does not return to the main menu when the chapter ends. Instead, it will flow through any succeeding chapters until the end of that title (i.e., movie) is reached. You can use whichever approach seems best.