Multiple Logins

I think its because you have the local machine's network administrator, the userid, and probably the default or allusers.
Could be someone logging onto the machine remotely?
You didn't indicate the users logged on (for instance do the names havethe same format for user naming conventions?)

There are several MS KnowledgeBase articles that may relate to your situation:

License Logging Service Decrements Licenses for Machine Accounts (Q300930)

Windows NT 4.0 Clients Take Multiple Terminal Services CALs (Q291936)

Several TerminalServices CALs Appear to Have the Same Computer Name (Q251386)

Another resolution may be to change from the Server Licensing mode to the Per Seat licensing mode. You can even turn off (and disable) the License Logging service. There is no requirement to run it in order to have NT 4 work properly.

Hope this helps.

Check which licensing method is good for you, or (you can find descriptions in help file of License Manager). Per seat is more better but you must have a number of CAL's equal with number of computers.
About your problem: inper seat you can manage licenses by grouping all licenses from a computer with Advanced options\new license group in License Manager (personal I made 2 groups: one for all admin accounts and one for all domain users and I set for these groups a no. of licenses equal with no. of computers). Also per seat don't limit you and allow more workstation than no. of licenses.
Per server is an economical way but hard to manage.

With no one else on the system and no remote logins even allowed.

If I login the one W2k work station the NT 4.0 Server will show there are eight distinct logins with a single User ID. And, if I login my work station, which only has my User ID- not even an administrator account, the NT Server shows three distinct logins.

If I try to disconnect just one of the logins all of the logins from the individual work stations are disconnected? Yet the NT Server treats them as individual logins for licensing purposes.