Far right groups are in fact far left (UK left reconsiders the BNP)

[Kralizec]

Every nation is at least to some degree socialist. You pay taxes, you get a national army and government services.

That's not a very useful definition of socialism you're using. Socialism is usually understood to mean:
1) the state is the sole employer and runs all production and services
2) democracy, since the people run the state all property is "collective"
3) all are equal so nobody's entitled to more wealth than others

A lot of socialists argue that no socialist state has ever existed because the USSR, China etc. were not democratic and because the upper party members were for practical purposes a privileged caste. I'd agree, but would add that the fact that it's been tried so often should show the futility of even attempting.
Most socialist parties have abandoned 3) because in developed societies the middle class is huge and they'd lose income in the case of total redestribution.

Fascism is an ideology that dismisses all enlightenment ideals and thus opposes both socialism and capitalism, the "third way" as Mussolini put it. The government manages the economy without taking away formal ownership from industrials using coersion. It runs all sorts of social programs to build up popular support without recognising that all people are equal. Most self-described socialists deny socialism and fascism have anything in common, but Mussolini and many of his contemporary supporters were former socialists themselves.