Omega-3 fatty acids is a supplement and has many health benefits. One of them is that it acts to prevent clots from happening in your blood. There are multiple studies showing this effect. Nonetheless, if you need to be on an anticoagulant I would not depend on just the omega-3 to provide that protection as there are no clear studies which demonstrate how much omega-3 you have to consume in order to have the same effect as taking Plavix.
It is not advisable to take Omega-3 and Plavix together because it may enhance the effect of the Plavix and make you more prone to bleeding. As Omega-3 is a supplement it is not strictly regulated by the FDA and as such there are no studies which have fully evaluated the safety considerations of taking Plavix and Omega-3 specifically. The general guidance that the FDA has given is based on the anti-coagulant property of Omega-3 that has been documented in scientific studies. This advice is that you should not combine and anti-platelet prescription agent with Omega-3 because there is a potential for increased risk for bleeding. You can however combine Prednisone with Omega-3 without much worry.