I don't know if there is a definite rule. However, this is from my experience : a) if there is more than election being held, and at different times, then the plural is needed. b) if there is only one election in one place, then normally the singular is used. c) if there is one election which is taking place in many places simultaneously, or one election for several different people or positions, you can use either.

I met this word on Duolingo in the phrase: "He wins the elections." Does it sounds a little weird - One person wins many elections?

Grammatically, it's simple. It's plural or singular. How many elections are there? One or many. One election, two or more elections. Although - having said that, elections themselves are not necessarily simple. If there was an election for one position, such as for a president, then it would be simple - an election. If, as happens in British systems, you have many electorates, each electorate could be considered to be an individual election. All those elections for all the electorates would typically be held at the same time, so you could refer to the entire process as either an election, or 'the elections'. So - it depends somewhat on the system...