Scientific realism is the belief that the theory or idea being explained is either true or false, depending upon whether the entities talked about by the theory exist and whether they are correctly described by the theory. This seems to be the popular position taken by most scientists in their attempts to explain the physical world around them. Support for this belief is that it is an inference to the best explanation available at the time, based upon the observable evidence. Positions taken against this belief tend to point out the existence of theories that were once considered successful, but are now regarded as false.
Anti-realism, as the name tends to suggest, is the belief that we should be skeptical about the physical world around us. Anti-realists embrace the following: 1) Nothing exists outside of the mind, and 2) We have no access to a mind-integrated reality, even if it does exist.
Irrealism, a metaphysical philosophy, seems to be a combination of the two, a "blend", if you will. The main belief here is that some part of the theory or idea may be valid, while others may be invalid. This belief relies on intuition, more so than scientific fact as it challenges science as fact.