Ken Saro-Wiwa. Photograph: Times Newspapers Ltd/Rex Features

In 1995, at a trial that resulted in his conviction and execution, the Nigerian writer and environmental activist Ken Saro-Wiwa vowed that the oil giant Shell would one day be brought to justice.

That day is looming large as a New York court prepares for a trial in which the oil giant Shell stands accused of crimes against humanity over its activities in the oil-rich Niger Delta of southern Nigeria.

Today, a last minute delay to the trial postponed the jury selection until next week. But when it does start, the trial will excite huge interest on the part of multinational companies and human rights bodies, because the outcome could have a bearing on the issue of corporate accountability and how far it extends.

Saro-Wiwa made his prediction days before he and eight other leaders of the Ogoni people were hanged by the Nigerian military regime in November 1995.

In a final statement at his own trial, which he was prevented from delivering, Saro-Wiwa said of Shell that "its day will surely come. The crime of the company's dirty wars against the Ogoni people will be punished."

When the trial does begin, relatives of the Ogoni nine, as the executed leaders are known, will be present in court as plaintiffs in the civil lawsuit against the firm. They and the other plaintiffs allege that Shell was an active participant in atrocities and abuses carried out by Nigeria's military police.

In addition to the alleged murder of the Ogoni nine, they also hold Shell partially responsible for torture, illegal detention, forced exile and shootings of hundreds of Ogoni protesters during the 1990s.

Shell has strongly denied the charges. In a statement to the Guardian, a Royal Dutch Shell spokesman in the Netherlands said the 1995 executions were tragic events that the company tried to prevent through appeals for clemency to the Nigerian government of the time.

"To our deep regret, that appeal went unheard, and we were shocked and saddened when we heard the news. Shell in no way encouraged or advocated any act of violence against them or their fellow Ogonis," said the statement.

The dispute between Shell and the Ogoni protesters stems from the company's extensive interests in the Niger delta stretching back to 1958. It now owns about 90 oil fields across the country.

From the early 1990s, non-violent protests began among Ogonis unhappy about the impact of oil exploration, which they said was destroying the environment that they depended on for fishing or farming.

Clearance work to make way for pipelines was decimating the world's third-largest mangrove forest. Oil spills were rife, polluting the land at a rate, campaigners said, equivalent to an Exxon Valdez oil disaster every year. Oil flares only made the pollution worse.

In 1990 Saro-Wiwa, a well-known journalist and activist, helped found the Movement for the Survival of the Ogoni People, bringing its case against Shell's destruction of the environment to an international audience. A peaceful protest in 1993 mobilised 300,000 Ogonis.

A year later the Ogoni nine were arrested on what were widely regarded to have been trumped-up charges. The men were tortured, beaten and then put on trial in front of a tribunal without legal representation. They were sentenced to death.

The civil action is slated for a federal US court under an obscure 1789 law that initially applied to piracy. In 2004 the supreme court ruled that it could be used by foreign parties to bring cases against defendants – including multinational corporations – in specific areas, notably torture and crimes against humanity.

So far very few cases have been brought to trial under the act, and none have proved successful for plaintiffs. But ­Jennie Green of the New York-based Centre for Constitutional Rights, which filed the case, said that human rights cases against corporations were still so new that no pattern had yet been established.

"Juries decide on the facts and we think we have a strong case that will convince them to hold Shell accountable for what they did. They were involved in human rights violations, participating, aiding and abetting," she said.

If it does go to trial, the case is expected to last up to a month, with Shell calling 11 witnesses and the Ogoni campaigners presenting up to 20. Among the latter will be Ken Saro-Wiwa Jr, the son of the executed leader, who will be pressing for compensation for his father's death.

For him, the case is not just an attempt to complete his father's search for justice. "It's the final stage for me," Saro-Wiwa Jr said. "In a sense I've lost the past 12 years of my life."

The other witnesses include the executed leader's brother, Owens Wiwa. He will allege that Brian Anderson, the then head of Shell's Nigerian subsidiary who is named as a defendant in the lawsuit, offered him a deal ensuring Saro-Wiwa would be released on condition that the Ogoni protests were called off.

The jury will be presented with evidence that the subsidiary told its parent company that Saro-Wiwa would be convicted and that he would never go free. They will also hear that two key witnesses at the trial that led to the hangings of the Ogoni nine later recanted, saying they had been bribed to give false testimony with offers of Shell jobs.

Karalolo Kogbara will also give evidence. She lost her crops when Shell bulldozed her village in 1993 to make way for a pipeline. When the villagers protested, Shell allegedly called for Nigerian troops, who shot her, causing her to lose an arm.

The company has yet to divulge its detailed defence, but it will be contesting every count on the grounds that the violence committed against the Ogoni was wholly caused by the Nigerian government and had nothing to do with its commercial operations.

The plaintiffs have not given any indication of the compensatory and punitive damages they are seeking, preferring to leave the matter, should they win, up to the jury. But such is the extreme nature of the charges that any award could possibly run into many millions of dollars.

Stephen Kretzmann, director of Oil Change International, who worked with Saro-Wiwa before his death, said the trial came too late for the Ogoni nine. But, whatever the outcome, he believes it will "send a message to multinationals that they have to obey local and international laws on human rights".

Saro-Wiwa Jr said he hoped that the jury would see that the oil giant's "fingerprints are all over this". He added: "For a long time Shell was able to operate with impunity hiding behind a military regime. Now it's time they were held to account."