How do I adjust the 'Create New Account' settings? New registrations are asked to create a password which is, in my opinion, excessively strong. Where do I go to adjust the password strength and other 'new account' settings?  When I looked in the listed modules, the 'User Module' was greyed out.

I am using Drupal version 6.
There were a few options for Drupal 6 so it's hard to give generic instructions. Check the module page for modules that include the word password and check for a "Configure" link.

Take Note: Drupal 6 is no longer officially supported by the community. While there are some places that are offering long term support for Drupal 6, you should plan to move to Drupal 7 or 8 soon.