Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that these animals are being given well water that is contaminated by an old oil field.
The good news is that the less refined an oil is the less is absorbed systemically and the less harmful it is. That means that crude oil from the ground is less toxic than highly refined gasoline.
It doesn't mean that the water is safe, and it would be ideal to not use this well water.
But if animals are only in the shelter for a short period of time there may be no long term effects.
Short term effects could be mouth irritation, drooling, and chewing motions, followed by coughing, choking, and vomiting and eventually diarrhea
due to the cathartic effects of the oil. Pneumonia due to aspiration of hydrocarbons into the lungs is usually the most serious consequence of ingestion of these materials, but is much less common with crude oil ingestion than with refined, lighter oils.
Chronic exposure could lead to anemia and central nervous system effects like depression, lethargy, tremors, incoordination and possibly seizures. Kidney or liver disease would not be common unless oil is aspirated in to the lungs and oxygenation of those tissues was poor.
The safest thing to do would be to collect a sample of well water and submit it to a toxicology laboratory for analysis. They can measure the concentration of oil as well as the types of oil present (different types have slightly different toxic effects) which will give definitive proof that this water is either safe or not.
In your state Texas A&M University has an excellent toxicology laboratory. Here is a link regarding water sampling:http://tvmdl.tamu.edu/tests/water-quality/
Best of luck with your concerns, I hope this information has been helpful.