First, you can make each "set" into one Cloze question. The Cloze syntax is not the most straightforward but its in core Moodle and has been for a long time. I've been doing more or less the same structure with Cloze since I started with Moodle. Then you can randomly pull a single Cloze question from a category and that will pull in your entire set.
The second option would be to install the Combined question type (and any other Open University plugins needed to make it work). You have to be able to install plugins for this to work. This works more or less like the Cloze option but has more flexibility.
I'm not sure that Mary's suggestion will work. I'm assuming that you mean that the questions within the set are not interchangeable with the other sets. If so you'll want to make sure that you pull an entire set, not pieces from different sets.