Is there any risk of illness from eating a food made with cooking oil?

Very litle. Because cooking oil is both a fat and an oil, it can grow rancid as a result of oxidation. Rancidity simply refers to decomposition, which adversely affects the flavor and odor of cooking oils. Though it can diminish the oil's nutritional value, rancidity isn't likely to make you sick. To delay the development of rancidity, processors apply a blanket of an inert gas, usually nitrogen, into large storage containers immediately following production--a process known as tank blanketing.   Proper storage at home can likewise delay the onset of rancidity.
 
Any fat, if extremely oxidized, can develop breakdown products which are harmful to your health. However, the flavor and odor of oils that are this oxidized would make them extremely unacceptable, and most people would not consume them. 
 
Recent studies have linked cooking oil to the formation of carcinogenic compounds at high cooking temperatures. Under these conditions, carcinogenic compounds are released when fat is oxidized. Other studies have linked poor arterial blood flow to consumption of foods prepared in used cooking oil. According to the studies, the foods constrict arterial vessels.
 
 
Source(s):
Wikipedia.org "Cooking Oil"
Answers.com "Cooking Oils"
Thirdage.com "How Safe is Cooking Oil?"
Susan Brewer PhD. University of Illinois, Department of Food Science and Human Nutriton