Task creation is handled by the appliance, and is only generated by an administrator operation (or could be when OneView refreshes hardware resources during its normal collection cycles.) The appliance is locked down, and thus you cannot write anything to the local OS, including log files. You could use an external API utility or script to collect events (based on severity, type, and resource), then log them somewhere else outside of the appliance. You could also use a State Change Message Bus client to "listen" to the SCMB queues for messages, and then take appropriate actions.
Examples are included within the HP OneView REST API Reference documentation (available on the appliance Help system, and http://hp.com/go/oneview/docs).
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