^ That was only because the Germans were so dominant at the time that the Italians had little hope of victories......except they ripped off a surprise every now and then.
Part of the problem with this is the number of different car types and race types. There wasn't much difference in 1900, but by WWII you'd have different formulas, sports car racing and specialized forms like the dirt tracks of Australia and America. Touring cars and Rally racing further complicate things post-war. You'd have to have a bunch of venues for this to cover everything, and then you have the fact that there would be countries that would regularly win in such events by spending more money and building better cars, thus forcing it into being a money contest not a contest of human skills and achievement. I can only see this if it was all identical cars. Perhaps the host city of the games lines up the vehicles?
Following the WI, if it was established in the 1936 Games (Hitler would like this - his Mercedes-Benz and Auto Union teams would dominate proceedings) and the first category was Formula 1, you'd have to get the best racetracks. For most of the Olympics host cities, however, this isn't hard. Berlin (1936) would host the events at the Nurburgring, in all likelihood. The London (1948) games would probably have the events at the Crystal Palace circuit in London, which hosted racing until 1972 IOTL, and so on:
1952 (
Helsinki): probably at Helsinki's own racing circuit, or at the Ahvenisto Circuit (IOTL not built until 1966)
1956 (
Melbourne): The Phillip Island racing circuit opened in 1956, so this one would be a natural.
1960 (
Rome): The Vallelunga Circuit is closest to Rome, but Monza would have more a viceral and emotional impact, plus you could also use it for oval races, too.
1964 (
Tokyo): Fuji Speedway would host the racing events, which would be spectacular - Fuji's 1960s layout was awesomely fast, and the scenery at the track is incredible.
1968 (
Mexico City): The Autodromo Hermanos Rodriguez would probably host this one, and its a good circuit, though its got nothing on Fuji and the altitude would slow the cars down.
1972 (
Munich): Undoubtedly back to the Nurburgring for this one, which would make for an excellent test for the drivers - the Nurburgring is a very, very tough circuit. Perhaps for this one they build the new Nurburgring a decade earlier than OTL in order to not get criticisms about the track's safety.
1976 (
Montreal): This one would be between Circuit Gilles Villeneuve in Montreal or Circuit Mont-Tremblant north of the city. Villeneuve is closer, Tremblant is the better track and has the better scenery.
1980 (
Moscow): This one is a toughie. Moscow would have to build a racing track here or make one out of the city streets, though a proposal involving Red Square was proposed for Formula One for 1983, but it did not come to pass due to bureaucratic crap. Might happen here.....
1984 (
Los Angeles): Laguna Seca Raceway would probably get the honors here, though Willow Springs and Long Beach could host, they are inferior tracks to Laguna Seca.
1988 (
Seoul): You'd need a track built for this one, too. But knowing how big the Koreans did the 1988 Games, I suspect that's not particularly an issue. The terrain around Seoul could produce a helluva circuit, too.
1992 (
Barcelona): Montjuich Park or the Circuit de Catalunya would have no issue hosting, but which one would be a debate. Catalunya is the better facilities-wise.
1996 (
Atlanta): Road Atlanta would get its Panoz-era facelift and host events. It's a fast track, and Turn 13 would scare a few guys in all likelihood.....
2000 (
Sydney): Eastern Creek circuit would probably get a makeover here, though it would be sooooo right if the Olympic Races got held at Bathurst......
2004 (
Athens): Circuit needed here, too. But again, lots of places where a big-time circuit would look really good.
2008 (
Beijing): The Goldenport Circuit is there, but it sucks. I can see the Shanghai F1 circuit hosting these, and that would be a show, though more for the track's facilities, because the layout isn't anything to write home about.
2012 (
London): Crystal Palace is long gone, but Brands Hatch is in Kent which isn't far away, so......
2016 (
Rio de Janiero): Rio's Jacarapagua Circuit was partially torn up for the Pan Am Games, but a circuit proposal was made to run international events on the small circuit and around the stadium facilities, which would work nicely.
And at least for Formula 1, I can see these being the medal winners......
1936: Tazio Nuvolari (Italy), Bernd Rosemeyer (Germany), Hans Stuck (Germany)
1948: Juan Manuel Fangio (Argentina), Stirling Moss (UK), Alberto Ascari (Italy)
1952: Stirling Moss (UK), Juan Manuel Fangio (Argentina), Alberto Ascari (Italy)
1956: Juan Manuel Fangio (Argentina), Mike Hawthorn (UK), Jean Behra (France)
1960: Bruce McLaren (New Zealand), Jack Brabham (Australia), Phill Hill (USA)
1964: Jim Clark (UK), Jack Brabham (Australia), Graham Hill (UK)
1968: Jackie Stewart (UK), Denny Hulme (New Zealand), Jacky Ickx (Belgium)
1972: Jackie Stewart (UK), Emerson Fittipaldi (Brazil), Francois Cevert (France)
1976: Mario Andretti (USA), Niki Lauda (Austria), Clay Regazzoni (Switzerland)
1980: Gilles Villeneuve (Canada), Nelson Piquet (Brazil), Alan Jones (Australia)
1984: Alain Prost (France), Niki Lauda (Austria), Stefan Bellof (Germany)
1988: Ayrton Senna (Brazil), Alain Prost (France), Michele Alboreto (Italy)
1992: Ayrton Senna (Brazil), Michael Schumacher (Germany), Nigel Mansell (UK)
1996: Michael Schumacher (Germany), Jacques Villeneuve (Canada), Mika Hakkinen (Finland)
2000: Mika Hakkinen (Finland), Michael Schumacher (Germany), Jacques Villeneuve (Canada)
2004: Michael Schumacher (Germany), Juan Pablo Montoya (Colombia), Fernando Alonso (Spain)
2008: Lewis Hamilton (UK), Kimi Raikkonen (Finland), Mark Webber (Australia)