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.
"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.
"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."
"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.
