Big Oil is facing a growing minefield of climate payout efforts, raising questions about how state and city plaintiffs will navigate new legal territory—and whether the fossil fuels industry will take a meaningful financial hit.

New York joined Vermont and enacted a “climate Superfund” law Dec. 26, which seeks $75 billion from the state’s largest polluters to address climate change over the next quarter-century. This comes as three tort suits have emerged from US states and cities just in the last two months targeting alleged misinformation campaigns about climate change and plastic pollution.

Climate Superfund bills and the ongoing …