Orient, who play in League One, claim that West Ham's move into the 500 million pound stadium will put their own existence in doubt.
Also, like Spurs, Orient say Newham Council were not entitled to provide a loan of up to 40 million pounds to the stadium company that will be set up to run the venue and from whom West Ham will rent the ground.
They also claim the Premier League has broken its own rules in sanctioning a move by one club close to the established home of another club in the area.
"We think the 40 million loan to West Ham is unlawful and we think it is illegal, and I think the Newham councillors have acted beyond their authority," Hearn told Reuters.
"We think it represents state aid, a subsidised development, which is staggering. I've never heard anyone giving state aid to a Premiership commercial operation before. We think they are both challengeable.
"I don't want anyone going into the stadium... (with an) unfair advantage over my club."
The Olympic Park Legacy Company (OPLC) in February approved West Ham's bid to move into the stadium after the 2012 Games rather than a rival proposal from fellow Premier League club Tottenham.
Orient are following up with judicial applications against the Secretary of State for Culture, Media and Sport, the Secretary of State for Communities and Local Government, the OPLC and the Mayor of London arguing the process had been flawed.
"I am being backed into a corner," Hearn said.
"The penalty for not doing it is that we get put out of business.
"I have money, but I have passion, I have nothing to lose as far as I'm concerned. I have sufficient funds."
He said his club had been ignored because the government was desperate to avoid the stadium turning into a white elephant.
"I think they just assumed... Leyton Orient would just keep quiet and roll over.
He pointed to the 130-year-old club being a community one, and said the only way West Ham could fill a 60,000-seater stadium was to offer cut-price tickets which in turn would eat into Orient's 4,000 fanbase and deter any new supporters.
Tottenham are contesting the use of public funds to help remodel the stadium after the Games.
Hearn said he had not liaised with Tottenham, and would have taken action if they had been chosen to take over the stadium.
