I have about 20 users on a Redhat box. Each user has its own group (which I believe Redhat does this by default when you set up a user). All of these users belong in the same group as the owner of the shared directories.

There are two shared directories. Whenever any of these users put something into these shared directories the files still belong to the original user.

Without changing the primary groups of the users, how can I set up the shared directories to change group ownership of any file/subdir placed in them to where it belongs to the group of the shared directories owner?

Are these directories, or samba shares? Are they subdirectories on a partition, or is each a mountpoint for a respective partition.

If they are samba shares, you can use the "force group" option.
If they are mount points for individual partitions, an they use a certain filesystem, then you could use the mount option "gid=".

If what you want to do is allow certain groups access, you could use the "setfacl" command to create a default group and permissions for the directory. Then files created in the directory will inherit the ACLs.

Some filesystems may support the grpid option. If the directory has the setgid bit set, files created in them will inherit the group ownership.