You can control sessions by your database's SESSIONS initialization parameter from the parameter file. But you also need to take care of the PROCESSES initialization parameter as sessions are proc *1.1+5. it's impossible to exceed this number of sessions unless you raise the parameter value.
SELECT name, value FROM v$parameter WHERE name = 'sessions';
This will show you the total number of sessions:-
SELECT COUNT(*) FROM v$session;
So answer to the question is Oracle can handle thousands of connections, but you need to take care of database resources.
Always use the below formula to set sessions and parameter:-
processes=x
sessions=x*1.1+5
transactions=sessions*1.1
select resource_name, current_utilization, max_utilization, limit_value from v$resource_limit
where resource_name in ('sessions', 'processes');