By default, any authenticated user is able to write to application event log. However only administrators can create new event Sources. If all event Sources are known at the service installation time, I recommend register those sources ahead of time, then you will be all set up. Registering is a simple call to EventLog.CreateEventSource.
If you need more flexibility on event sources, you can customize permissions. Those defaults could be customized by tweaking a registry key:
HKEY_LOCAL_MACHINE\System\CurrentControlSet\Services\Eventlog\Application\CustomSD
A process described in this KB Article. A wevtutil tool, which is part of OS, available on Server 2008 and above, makes it a bit easier than going through regedit.