I just went through the process of setting up SNMP checks on some Synology devices. Two suggestions:
1) Search the Nagios Exchange for a script for your specific device. You're probably not the first person to want to monitor whatever it is and chances are good that someone has already written a plugin.
2) Try the generic check_snmp plugin, but know that you're going to have to enter more than just a couple of arguments for it to work. By default, you'll just have the check_snmp and the host (-H <value>). To get my check to work, I had to enter this whole string in the single argument field. "-C public -m '/usr/share/snmp/mibs/SYNOLOGY-SYSTEM-MIB.txt' -o .188.8.131.52.4.1.65184.108.40.206 -w 60 -c 70"