They have a clever name to their party, but they are definitely controversial as a whole. Without living in Greece, you probably don't see the whole picture of why they exist and don't get all the facts on what their members do - especially by researching on Wikipedia. There are undoubtedly extremists in the party, but I seriously doubt such a blanket statement can be made about them as a whole.
You need to look at the situation in Greece and out it into perspective before passing judgement on their stances. For instance, The civilization of Greece has existed for millennia as a collection of city states. In more recent times, they have evolved into a unified nation with a tax-and-spend government, which has been running them further and further into debt to the point that they are renting out ancient monuments to campers to try covering some of the expenses. Their unemployment rate is something like 25%, and people feel entitled to their piece of the pie from the government are going with nothing! as the government prepares for a default on its debt. The European Union is ready to boot out Greece, since the nation is dragging everyone down.
So, because of all this suffering of the people, new political parties are arising that promise to make things better. This can be scary (NAZIs, Bolsheviks, etc.) or hopeful (American Revolutionaries, etc.) if you look at history. The Golden Dawn are opposed to immigration for similar, yet still different, reasons from extremist American opposition to all immigration (which is very different from opposition to illegal immigration and asylum-based immigration). Europe has seen a large growth in the legal immigration of Turks over the past couple generations. These people have come in a perfectly legal manner to seek better lives for their families. Still, there has been growing opposition to them over the past several years, because they hold their own culture and have large families that have a higher rate of government assistance than the families of other Europeans. The European-style socialism is what has been dragging down that nations of Greece, Spain, Italy, France, and others. People want a scapegoat, so they choose immigrants. (Hopefully this will not lead down the same path as Weimar Germany.)
So, in Greece specifically, some factions, like the Golden Dawn, want to stop immigrants from coming to the country, since they see immigrants as contributing to the problem. More extreme members try to take matters into their own hands (kind of like Occupy Wallstreet in the US) instead of seeking a peaceful solution (more along the lines of the TEA Party in the US).