One solution is to make all your support categories restricted (not public). This won't stop the spam per se, but will make it far less useful for SEO. Run the following SQL using bin/ljdb:
update supportcat set public_read='0'
If what you want or need is to stop the spam completely, not just hide it, the best way depends on whether it's coming by email or the web form.
If by email, make sure bin/worker/incoming-email isn't running, either by hand or because you listed it in workers.conf. (With the change in layout, I'm not sure whether it lives in etc or ext/local/etc, so you may need to check both locations.)
If through the web form (and not letting your server run except when you need it isn't an option), I think your only solution is setting up CAPTCHAs, but I'm not sure how to do that.
no subject
If by email, make sure bin/worker/incoming-email isn't running, either by hand or because you listed it in workers.conf. (With the change in layout, I'm not sure whether it lives in etc or ext/local/etc, so you may need to check both locations.)
If through the web form (and not letting your server run except when you need it isn't an option), I think your only solution is setting up CAPTCHAs, but I'm not sure how to do that.