What does 系 in 日系车 and 德系车mean? Does it mean style here? If so, the Chinese word should have been 风 as the shortened version of 风格.

The other meaning might be department, as in a college, like department of foreign languages, but it is obviously impossible in this context.

If it means "made in Japan" or "made in Germany", many vehicles are actually made in China, if they are imports, could they be so named as 日系 or 德系？
系 could be 'a system', 'a series' in its original meaning.

In this case, 系 could be understood as where those car brands from.

Toyota, Honda cars are 日系車. GM, Tesla cars are 美系車. BMW cars are 德系車. Other car brands in Europe except for Germany are 歐系車. 德系車 is independent because BMW and Mercedes-Benz are much famous brands in the world.

Another case, Volvo was sold to Chinese firm. We still call Volvo as 歐系車 because the brand Volvo was started in Europe.