Is there a naturalist in the house?

It's possible that NO ONE is dumping intestines in the park. It is spring, and the intestine-looking things in the park may be toad spawn, aka toad eggs.

this site has been helpful
http://www.umaine.edu/WaterResearch/FieldGuide/inthewater.htm#eggs

and gives the following description :-

- long strings of hundreds of eggs together.
They seem to be suspended in jelly
What is interesting is that the eggs are suspended in a coiled helix shape.
They all seem to be attached or draped around the plant life, and only in about 1 foot of water...."

Interestingly toad eggs and tadpoles are poisonous to fish and most fish learn this
quickly but some fish are not that smart. So a dead fish nearby might not be so strange and horrible at all.

Doesn't explain the dead chicken heads, but it makes them into a smaller problem. So9metimes that's the best you can do.