The centre-backs are in Giovanni Trappatoni's squad to travel to Wembley Stadium to take part in a friendly which marks the 150th anniversary of the Football Association.
Leicester City defender St Ledger says he wants to give Irish fans something new to remember by upsetting Roy Hodgson's England side.
"We all remember the games from 10, 15, 20 years ago, we want to give them something new to remember," he told reporters after a session at Watford's training ground.
"That's what we're trying to recreate. These are games that, although it's a friendly, they'll be remembered for a long time. If we are part of a winning team then it's going to a massive occasion for the country. It's something to look forward to and relish.
"It's almost once in a life time. Every international game is an honour to be involved in but I suppose it's even more significant when it's England. Hopefully I can be part of a winning team and create some new memories.
|15/1||Sean St Ledger is 15/1 with BetVictor to score anytime against England
Toronto defender O'Dea hopes the match does not replicate the meeting between the two sides at Lansdowne Road in 1995 which was marred and abandoned over crowd trouble - though he believes it will no longer an issue.
"I don't know, we'll have to wait and see," he replied when he was reminded of the occasion.
"I wasn't there, I watched it on TV, but obviously I hope we can create some new positive memories. Football has moved on, I certainly hope it doesn't happen again. Hopefully it's just a good game of football.
"Yeah, I do [have memories of the fixture] but that's in the past now, it's time to create some new history."
Despite missing the entire Premier League season at Aston Villa, centre-back Richard Dunne has also been included in the squad. The 33-year-old is more than welcome competition according to St Ledger.
"He's our leader," the 28-year-old continued. "He's got this beast in him, I suppose. He could be out for 10 months and he comes back looking like the same player. As soon as he gets his match fitness back he will be important for us.
"He's fantastic to play alongside, he's a good talker and he talks you through the game. He leads by example."
Meanwhile, O'Dea, who has settled in quickly to life in the MLS with Toronto, is also hoping to earn a place in Trappatoni's starting XI after a positive first season at his new club.
"After going out on loan a lot, playing games did me good," said the 26-year-old. "The MLS is maybe not looked at in a high regard but personally I'm happy with the experience I had."
"Until you go out there and actually see the league it's hard to understand. It's completely false what people believe. At Toronto I play in front of larger crowds than I did in the Championship and the Toronto fans are like European [fans] in the way they support the team, it depends where you are. We're really well supported."
O'Dea wants to end the season on a positive note and is eagerly awaiting the challenge of fixtures against England, Georgia, Spain and the Faroe Islands.
"It's important we sign off on a good note this season and pick up a good result [against England]. Obviously the next three games are hard fixtures against good opposition but we need to test ourselves against top sides and do better."