This is a very interesting question, that has been extensively studied and has received great attention. As such, it has often been vandalized by generic press, leaving people quite confused on the matter.
That antioxidants have physiological effects I would say needs no proof: our body utilises antioxidants such as ascorbate (vitamin C) to keep down the amount of free radicals, as can be confirmed by any basic physiology textbook (I can provide references if you need).
To get to the actual point of your question: do antioxidants have the "ability to prevent strokes"? I don't know if the article you read specifically used those words, but this is the type of bad "generic press talk" I was referring to...
Antioxidants do not prevent stroke. You can live a super-healthy life, take tons of antioxidants, exercise every day and still have a stroke.
What certain antioxidants can do is to reduce the possibility of having a stroke, which is a very different thing. This is mostly due to the fact that oxidative stress is a risk factor for different cardiovascular diseases.
In the same line of thought, certain antioxidants, in certain regimes and certain situations can help fighting cancer. They DO NOT CURE cancer by themselves, I cannot stress this enough. Again, the idea is that free radicals can damage DNA increasing the risk of cancer. Free radical do not provoke cancer, but they can be a risk factor.
Same for neurodegenerative diseases and many other illnesses where antioxidants can help in certain cases.
It is difficult to generalize because stroke, cancer, neurodegenerative diseases are very broad category of illnesses, that can have the most disparate etiologies. So free radicals are not always the issue and antioxidants are not always the solution. Also, free radicals are actively used by our bodies (e.g. during immune responses) so excess antioxidants is not necessarily good.
The scientific literature at this regard is simply huge and it would be difficult to have a complete bibliography here. Here's a sample of papers and reviews at this regard, if someone who is more in the field knows better papers/reviews please feel free to update my answer (sorry most of these are limited access papers).
Air pollution: mechanisms of neuroinflammation and CNS disease. - Block and Calderón-Garcidueñas, Trends Neurosci., 2009
Oxidative stress and endothelial dysfunction in cerebrovascular disease. - Chrissobolis et al, Front Biosci., 2011
Oxidative DNA damage in mild cognitive impairment and late-stage Alzheimer's disease. - Lovell and Markesbery, Nucleic Acids Res., 2007
Mitogenic signaling mediated by oxidants in Ras-transformed fibroblasts. - Irani et al, Science 1997
c-Myc can induce DNA damage, increase reactive oxygen species, and mitigate p53 function: a mechanism for oncogene-induced genetic instability. - Vafa et al, Mol Cell 2002
and there is many many more.
Not all antioxidants are good, however. For instance, this paper talks about the role of the transcription factor Nrf2, a factor which is involved in the physiological control of free radicals (so we can, by extension, call it an antioxidant inducing factor). The authors show that excess activation of Nrf2 does actually induce tumorigenesis rather then prevent it.
Oncogene-induced Nrf2 transcription promotes ROS detoxification and tumorigenesis. - DeNicola et al., Nature 2011