Even for the Lincoln Centre it was an unusual show, and an unscheduled one. Several hundred protesters turned up outside the arts complex on Manhattan's Upper West Side last week for the guerrilla screening of a short film. From a hotel on the other side of the street, a video was projected on to the centre's walls. The unwitting stars of the films were David and Charles Koch, the reclusive rightwing billionaire brothers whose secretive empire and network of influence and funding is emerging as a liberal rallying cause in America.

As bemused theatregoers watched the boisterous crowd, the videos depicted facts and figure showing Koch support for Tea Party groups, global warming sceptics and thinktanks seeking to strip away regulations on the environment, cut social security and oppose healthcare reform. On the David H Koch Theatre in the complex – renamed when one of the brothers donated $100m (£62m) in 2008 – activists climbed a ladder to post a giant sticker above the sign bearing Koch's name. "I am the Tea Party's wallet," it read. When the police vans finally arrived, the activists had gone.

For Koch Industries, one of the largest private businesses in America, it was another attempt by liberal groups to drag it into the public eye over accusations that it is corrupting US politics in pursuit of its business interests. There have been lengthy magazine articles investigating its activities, growing protests and a legion of bloggers scouring the company's every move.

At the forefront of the movement is the unlikely figure of Hollywood director Robert Greenwald, 65, who brought the world the Olivia Newton-John dance movie Xanadu. Greenwald reinvented himself as a leftwing documentary maker, and has his focus on the Koch brothers. His Brave New Foundation group organised the Lincoln Centre film show.

"David Koch spent $100m to put his name on that theatre, but we want people to understand what it really should be named," he told the Observer.

Brave New Foundation, with a team of 15 including three full-time researchers, is running a web competition where suggestions for a new sign are plastered over a picture of the theatre. "Treasonous Plutocrats R Us" and "Evil Greed Incarnate" are some of the entries.

Greenwald said that the popularity of the contest is another way to keep public attention on the brothers. Indeed last week Jack O'Dwyer, a leading Manhattan PR professional, called on the Lincoln Centre to drop the Koch name. That was music to Greenwald's ears. "The Kochs have always been very smart. They did not need the spotlight. But the more people we can impact with our actions showing what the Kochs have been doing, the better off we will be."

Greenwald is determined to make the fight personal. His activists have found five homes of the brothers in the US and filmed themselves knocking on the doors, from the ski resort of Aspen, Colorado, to Palm Beach in Florida. The homes are profiled in "luxury porn" detail and juxtaposed with the hard times of working-class Americans. In one scene three financially struggling pensioners picnic on the beach outside a Koch mansion and wonder why anyone would need a house so big. In another, a researcher ambushes David Koch at the Economic Club of New York and asks: "How many houses do you really need?" The stone-faced Koch rapidly retreats behind a security guard without a word.

The personal tactics have brought Greenwald criticism, but he is unconcerned. He says that the political activities and donations of the brothers have affected the lives of millions of less wealthy Americans. "The least we can do is ring their doorbell. What they are doing is hurting people's lives. Ideology has consequences."

Anger is focused on the mix of conservatism and libertarianism, especially in economics. The sprawling Koch Industries has vast oil and energy interests. The brothers, each worth an estimated $22bn, are joint seventh on Forbes magazine's 2011 list of the richest Americans.

Their money helped start Americans For Prosperity, a Tea Party-linked organisation that has campaigned vociferously against Barack Obama's healthcare reforms. It admitted helping to organise anti-union moves by the controversial Wisconsin governor Scott Walker, which led to some of the largest protests in recent American history.

The Kochs have also given millions to thinktanks and groups that fight environmental legislation, especially to oppose the scientific consensus on global warming and try to lift regulations on air pollution and potentially dangerous chemicals. They believe in drastically cutting the role of government and slashing benefits such as social security.

A recent report on the Politico website detailed how they planned to spend $88m in the 2012 election supporting conservative causes and politicians.

The Kochs share the Tea Party view that Obama is a threat to the American way of life. Last week David Koch made a rare comment to a reporter from New York magazine, calling Obama "a hardcore socialist". "He's marvellous at pretending to be something other than that, but that is what I believe he truly is, a hardcore socialist. He's scary to me," he added.

There is nothing illegal about the Kochs' political activities. Greenwald concedes they have every right to fund whatever organisations they like.

Some groups have said however that their business practices are sometimes the opposite of their public campaigns. A non-partisan Washington watchdog group, the Centre for Public Integrity, reported last month that Koch Industries' ethanol business enjoys high incomes thanks to government subsidies, despite their disapproval of such policies. Equally, while they oppose a cap-and-trade system in the US to control carbon emissions, the trading arm of Koch Industries makes millions in Europe from such a system.

The report also detailed their lobbying interests. From $857,000 in 2004, Koch Industries spent a staggering $20m in 2008 and $20.5m from 2009 to 2010

The company employs about 30 people in Washington seeking to influence more than 100 pieces of federal legislation. Greenpeace has expressed concern at the lobbying activities: "Organisations funded by Koch foundations have led the assault on climate science and scientists, green jobs, renewable energy and climate policy progress," it said in a report on the brothers in March.

Last week it was reported that a Koch foundation had funded two academic posts in the economics department of Florida State University – with the proviso that it would decide which candidates could be considered. Giving such power to a donor is an unusual move, especially at a public university. It also emerged that 60% of the university's suggestions were vetoed by the Kochs.

Not surprisingly, the brothers are fighting back. They rarely respond directly to their press critics. Emailed questions from the Observer to a Koch Industries representative received no response. But some reporters have been approached by PR people hired by the brothers to put forward their point of view.

The Kochs have also used more hardline tactics. One of the most revealing recent articles was a long exposé in the New Yorker by Jane Meyer. But when the report was nominated for a national award, a Koch executive wrote to the American Society of Magazine Editors criticising it for considering the article.

The brothers also sued pranksters who set up a fake Koch Industries website and sent out a bogus press release. Though a Utah judge dismissed the case, such lawsuits could easily be seen as a threat to others not to do the same. The Kochs also apparently bought online advertising against the Centre for Public Integrity report so that Google searches for it would also find statements rubbishing the claims.

Despite such efforts, the anti-Koch campaigners are unlikely to go away. Greenwald – whose previous targets have included Fox News, Walmart and former New York mayor Rudy Giuliani – says that he has at least seven more anti-Koch videos in the works.

Greenwald said the threat of a Koch backlash against his organisation was a concern but that he would not be intimidated: "The Kochs are the poster boys for a system that has become deeply unbalanced. We know that they are not happy with what we have done so far. They are going to be a lot less happy as we go on."