I'd like to use the snmpset command to get my router to execute an EEM script. Are there OIDs that are associated with EEM scripts that could help me achieve this?
Although EEM has associated MIB, it has a single read-write variable: the size of the history table. It's thus not possible to use EEM MIB to trigger EEM events. However, EEM 2.4 added support for SNMP notification events, which you can use to trigger EEM applets based on incoming SNMP traps/informs.
You can therefore use the event snmp-notification command on a router and the snmptrap command on a Linux host to remotely trigger EEM applets.