The Independent MP for Sheffield Hallam used his maiden speech to tell of his "pride" in representing disabled people, as he said he was Parliament's "very first autistic MP, as well as having cerebral palsy and other disabilities".
And he spoke of what can be learned from the teachings of Jesus, saying he "forgave those who truly repented".
Mr O'Mara was suspended as a Labour MP over sexist and homophobic comments before quitting the party, claiming he had been unfairly treated.
He told the Commons: "Mr Speaker, thank you - in fact, everybody thank you, you've all been terribly patient.
"I'm delighted today to finally be able to make my maiden speech as the MP for the constituency where I grew up, Sheffield Hallam.
"I was elected a year ago as Hallam's first Labour MP but due to mistakes I made when I was young, and for which I am truly sorry have hurt a lot of people, I've been unable to speak in the House with confidence until now."
Mr O'Mara's maiden speech lasted for four minutes, and while MPs usually gather around their newly elected colleague for the occasion, he stood alone at the end of the rear opposition bench.
He delivered the speech during a general debate in which MPs can raise any matter they want ahead of the summer recess.
Mr O'Mara said it was "an honour" to have the chance to "represent our country's disabled people in addition to serving my constituents".
And he paid tribute to his Liberal Democrat predecessor Sir Nick Clegg for his "admirable and steadfast belief in the value of our membership in the European Union" and commitment to multiculturalism, noting he shared both of these.
Mr O'Mara said he was "very proud" to call Sheffield home, describing the city as the "epitome of multiculturalism".
And the Independent MP praised the sports stars which have emerged from his constituency, including "the best right-back in football" Kyle Walker.
He offered the warm tribute to the England star "even though I am an Owl and he is a Blade" - in recognition of his support for Sheffield Wednesday and Walker's for Sheffield United.
The backbencher also spoke of what can be learned from the teachings of Jesus, although said he considers himself "a man of science".
Mr O'Mara said: "He was a man who forgave those who truly repented and he shares my belief that our utmost human priority should be helping those who are most disadvantaged and vulnerable amongst us."
The Sheffield Hallam MP concluded his remarks by asking his constituents, all political parties and everyone in the country to join him in "prioritising these principles".
He added: "I promise that I will do my utmost to help all those in need of help within my constituency and to champion the cause of equality.
"When I return to Parliament in September I shall do so with renewed vigour and an unwavering commitment to social justice and look forward to being the best MP that I can possibly be."
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