Is it wise to invest in the American market knowing that most of its stocks are highly overpriced and also should start to buy commodities ?

Nobody can know, whether these expensive appearing U.S. stocks are overpriced.

since entering Your question (see chart) and being subjected to 2 market 'crashes' already (end 2018 and 02/2020)

the U.S. SP500 still appreciated 5-6% as opposed to

the Strait Times Index: minus 5-6%

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More than one year had passed since this question had been asked, and the S&P 500 index had been recording fresh highs, shrugging off the bearish effect of a US-China trade war.

So stocks thought to be overpriced back in Sep 2018 now looked CHEAP by today standards lol.

If your cant pick stocks, then time in market is always better than timing the market