Default soapui-log4j.xml has appenders for soapui.log, soapui-errors.log files.
So, tried to play there and below is the screen shot and marked changes from INFO/DEBUG to ERROR. Then restart soapui, do some activity and see the difference in those log fies i.e., nothing in those files except if there is any error unlike earlier. May be you can preserve those logs before restarting soapui after log4j changes, so that can be compared later.
I believe, similar appender can be added to groovy script log as well - could not try. Please post the result if you get a chance to try.
And also believe that you may change at logger level, just below the lines of attached screen shot. Please keep a back of original file before your changes for testing and revert them when you want the default settings.