Windows event logs are logs of system events maintained by Windows operating systems and can be accessed locally and remotely using the Event Viewer MMC snap-in (start->run->eventvwr). A basic Windows system has three logs, system, application and security; a server with additional roles may have additional ones. Within each log events can have different severities.
Syslog is a standard method of recording system and other events popular on Unix systems but also supported by other devices such as network switches and routers. Basically you have a (unix) system running the syslog daemon and you tell the other parts of the operating system on that box plus your other boxes and devices to send their events to that daemon. The daemon then categorises and records them. Again you can have various levels of severity for different events.
SNMP is an industry-standard protocol for obtaining health and performance statistics from a variety of network-connected devices. Within the SNMP standard SNMP traps are defined as unsolicited messages sent from the monitored device to the management station when some event occurs that you want to be informed of (such as low disk space, high network utilization or a system restart). You need an SNMP trap receiving application on the management station to receive the traps and undertake some action (such as write them into a log, sound an alarm) when they arrive