The biggest risk of staying near an oil well is pollution. A lot of activities go on when oil exploration is taking place. The most likely is a spill which degrades the environment badly and is very expensive to clean up. A very good example is in the Niger Delta area in Nigeria.
image source: gCaptain
The Ogoni oil spill is one of the worst in the world. Between 1976 to 1991, more than 2000 oil spills occurred in the area where millions of barrels sipped into the soil. Oil spills damage the soil and make farming impossible, the same is the case for fishing. It typically snatches the livelihood of millions from them.
As I write this answer, Ogoni hasn't been cleaned up. Its a typical example of the failure of the Nigerian government over the years to get justice for these people.
Before I digress further, another danger is gases escaping into the atmosphere which can cause acid rain. Acid rain typically occurs from time to time in the Niger Delta area. Acid rain causes large scale corrosion and damage to crops.
Image source: The Environmentalist
Gas flaring is another hazard that releases green house gases into the atmosphere. Its not very common in other parts of the world because these gases are liquefied and stored. In Nigeria this hasn't yet been achieved, so gas flaring is still a concern and has been going on for more than 60 years of oil exploration in Nigeria.
What a waste.
Generally if a person is staying and living near oil and gas exploration well, then he/she is subjected to noise, emissions from the old pads every time. It may not have any sudden or temporary effect. But over a period of time it may develop serious passive concerns to your health.
Statistics shows that such people suffer from cardiovascular disease, higher blood pressure etc. The extent of hazard also includes chronic inflammatory disease like asthma or arthritis. Exposure to environmental stresses have lasting impact on health if one continues to live under such exposure for a prolonged time and it may adversely deteriorate health further.
Further the particulate matter emitted from oil and gas operations may result in intense complications and more severe cardiovascular diseases and death in extreme cases. One may also suffer from arterial stiffening as a long term consequence to such exposure.
Thank you and Have a great day.