You could script this with your favorite language (perl, python, etc.) or use curl/wget. All of the CGIs can be run from the command line as well, but you'll have to set the REMOTE_USER
env variable.
The params are absolutely encoded in the URL, but the stock Nagios web interface uses frames, so you don't see them. View the actual frame that the report is in, and you'll see the GET params.
You can also use a browser add-on like Live HTTP Headers (for Firefox) to show you exactly what is being requested. For example:
GET /cgi-bin/nagios3/avail.cgi?show_log_entries=&host=all&service=all&timeperiod=last7days&smon=11&sday=1&syear=2013&shour=0&smin=0&ssec=0&emon=11&eday=25&eyear=2013&ehour=24&emin=0&esec=0&rpttimeperiod=&assumeinitialstates=yes&assumestateretention=yes&assumestatesduringnotrunning=yes&includesoftstates=no&initialassumedservicestate=0&backtrack=4&csvoutput=