Now, three decades after German police detained him at a torch-lit protest by a group aping the Hitler Youth, Strache, 48, is the besuited, statesmanlike head of Freedom Party (FPÖ), rejecting all extremism.
But it remains to be seen whether the man who in 2016 called German Chancellor Angela Merkel “the most dangerous woman in Europe”, has mellowed enough to be part of a coalition government in a European Union member state.
When the former dental technician took over the FPÖ in 2005 aged 35, the movement was a mess. Jörg Haider, its controversial but magnetic leader from 1986-2000, had broken off to form his own party.
But “HC”, his striking blue eyes matching the party colours, restored its fortunes and on Sunday the FPÖ is predicted to win around 25 percent of the vote — more than double Alternative for Germany's score last month.
When the FPÖ last entered government in 2000 under Haider, there was uproar in Europe. This time the reaction is likely to be muted, with Europe more used to populists and the FPÖ seen as having moderated.
Indeed, early in Strache's leadership, FPÖ posters screamed “Daham statt Islam” (“Home not Islam”) but now they are more subtle.
In this campaign, the main messages are “Fairness” — an elastic term encompassing everything from lower taxes to scrapping benefits for immigrants — and opposition to “Islamisation”.
Strache has moved to clean up the party's image by suspending members for anti-Semitic behaviour, like a local councillor for a “Heil Hitler” salute this month.
But not everyone is convinced. Last month a group commemorating Nazi camp victims published a list of what it said were at least 60 anti-Semitic and racist incidents involving FPÖ figures since 2013.
“If they really changed their ideology, it is a question they can only answer themselves,” said analyst Alexandra Siegl.
“I would say they changed their tactics and their strategies mainly.”
Its manifesto vows “no more immigration until further notice”, pamphlets rail against criminal immigrants and the FPÖ wants all integration efforts for refugees to stop — because they are only here temporarily.
“No, Islam is not part of Austria,” Strache, back in jeans and traditional loden jacket and accompanied by his model wife 20 years his junior, told a typically beer-swilling, flag-waving FPÖ rally recently.
“Strache is the counterweight to Angela Merkel whose 'welcome culture' is destroying Europe,” one FPÖ supporter told AFP, not wishing to give his name.
He appears ambivalent at best on Europe, calling Brussels a “bureaucratic monster”, believing Britain will “probably be better off after Brexit” and saying EU sanctions on Russia must be lifted.
“Strache knows he has to act the statesman if the FPÖ wants to get more than 20 percent,” Nina Horaczek, an award-winning journalist who wrote a biography of Strache, told AFP.
“But with their programme and all their talk of 'mass invasion' and the spreading of fear of an upcoming 'civil war' in our country, it's obvious they remain radical.”
Strache has also made deft use of the internet, with more Facebook “fans” than any other party leader, and until earlier this year he was on a roll.
In December, the FPÖ's Norbert Hofer came close to being elected Europe's first far-right president since 1945 and the party was topping national polls.
But in May Sebastian Kurz, just 31, took over the centre-right People's Party (ÖVP) and leapfrogged the FPÖ into first place in the polls — thanks partly to moving rightwards and stealing many of Strache's policies.
Strache, poking fun at “late bloomer” Kurz and presenting himself as the “visionary”, has struggled to recover, dashing his dreams of coming first and being chancellor — barring a surprise on Sunday.