I think changing the SESSIONS parameters is not the right way.
You should increase de PROCESSES parameters that is directly related to the maximum number of sessions you can have.
In a "normal" database configuration, each user session is "attached" to one process. So, if the PROCCESS parameter is set low you will be running out of processes and getting the error "ORA-00020: maximum number of processes exceeded".
Also, you might try to setup SHARED SERVERS that is another Oracle feature that pools several processes an share them among several (a lot) user session. So, as an example, you could have only 10 processes handling the load of 200-250 sessions. Well, this is another topic but if you're interested we can talk more about it.
But for now:
1. You should increase the PROCESSES parameter
2. Quit the SESSIONS parameter. Oracle will calc this value from the PROCESSES parameter (1.1 * PROCESSES + 5)
3. Parameters like LICENSE_MAX_SESSIONS and LICENSE_MAX_USERS should be 0 (ZERO) that means unlimited (if you have this kind of license from Oracle).