I would leave it for a while to rot down where it is, then turn it in with a rotavator once it's drying, but before it sets like rock. You need to keep off clay soil while it's wet, or you compact it even more than the pigs have. Having pigs on clay ground causes an impenetrable hard pan at the depth of their feet, so that needs to be broken up before you can grow crops.
For possible contamination with fluke, worms and other parasites, pigs are very close to humans as I'm sure you know, so yes, I would say there is a chance of the veg having eggs on when harvested. I wouldn't risk it this year, unless you are absolutely certain that your animals are parasite free.