By "catalog", I take it that you mean your "many images referenced by the one catalog".
You have two options:
(1) Move the images from inside of Lightroom, or
(2) move the files from outside of Lightroom using your OS tools then inside of Lightroom reconnect all the broken links.
Which one to pick would probably depend on what your source directory trees look like and on how similar you plan to make the destination directory trees.
Leave things as they are. Lightroom doesn't care if the photos are on different drives, it works perfectly fine in that case. If you organize using keywords and other metadata, then you won't ever care either that the photos are on different drives. It's a very simple approach.
If you are consolidating because you are moving everything to a new or different large hard drive, you have a couple of options.
Option 1: you can drag/drop folders in the Lightroom library module. There have been reports by users who have done this that all the images don't get moved, and then they have to devote considerable time to locating the missing images.
Option 2: you can move folders of images to the new hard drive using your operating system. When you display the folder that you have moved Lightroom will tell you that it is missing. So you have to show Lightroom were the folder is now located.
If you have a lot of images and folders to move, it is my opinion that option 2 is the better option. The operating system seems to do a better job of moving the files. But you have to take the time to point Lightroom to the folders on the new hard drive. It isn't that time-consuming, but it will have to be done.
If you're going to do this move, I strongly suggest that you organize your folder tree so that you have one main folder with subfolders for different years or different projects or what ever within that main folder. Then, in the future, if you have to make such a move again you only have to move the main folder and then find that missing folder in its new location and everything else will be linked as it should be.
Thank you Jim, this seems to be along the right lines of reasoning. My five terabytes of of hard drives, scattering raw files along with backups, outputs from the jobs, an iTunes library and miscellaneous video projects has become too much of a patchwork quilt. My solution was to buy two new five-terabyte drives (one for backup) and move all the images onto onto a single 5 TB drive. I have tried Option 1 before, and found that it was messy. Option 2 might be the better. The operation will be somewhat lengthy as there are 169,000 images in the master catalogue.
In the meantime, I have found this web page How to Consolidate Your Photos in Lightroom - Pixel Training and it seems to give an interesting Option 3.
I am slo pondering, once the images are all moved, is it better to store the .lrcat file on the computer hard drive, on the same external hard drive as the images, or on a different external hard drive?
As this represents a new beginning, I would like this to be done as cleanly as possible.
It really doesn't matter where the catalog file is stored. I don't think there is a right answer. The default location when Lightroom is installed is to put it in a Lightroom folder in the pictures folder on Windows. Whether or not that is the "right" location is probably up for debate. If you decide to move the catalog then I think it's probably best to move everything in that folder to the new location.
Moving with the OS is easiest. However before you do that ensure that on each drive your folders are all in one top level folder so you have to move only one and relink in Lightroom only one folder for each drive.
In the screen shot below of my "2 Images" drive I have all the images in the "Image Files La Cie" Folder so I only have to move that folder to another drive.