For a quick check, if you have access to the database via adminer or phpMyAdmin, go look at the mdl_question_attempt_step_data. Click on the field labeled, 'value' so the answers are all sorted. Scroll through the table, 'duplicates' will be bunched together. This is actually kind of limited as you will only be able to see a few words at the start of each essay answer, and if there are a LOT of quizzes, the table will be rather large.
A better way if you have the Ad-hoc Database Queries plugin stealled, would be to set up an ad-hoc query for that table and others, so you can have it also automatically tell you the name of the students for each entry. Plus, once you make the ad-hoc query, it is always just a couple of clicks away, any time you want to run it. As part of the
query for the database, sort the essay answers ascending or descending
and it will then put 'duplicates' together making them fairly easy to spot. You can also set up the query to scan for a particular quiz to cut down on the amount of results.