He smiles when he talks about how this team has achieved what no Kenyan team has ever done in any sport outside of athletics.
He laughs when he talks about Amitabh Bachchan and how thrilled they all are with the fact that he will be coming to watch the semi-finals.
He impulsively breaks into song - Tezaab's 'Ek, do, teen' - when asked if Hindi films popular in Kenya.
And he speaks more in anger than regret when he says, "We have done well in this tournament and people still say we were lucky and should not have made for the semi-finals. Is it our fault that New Zealand forfeited their match?"
"We are in the semi-finals by virtue of having beaten three Test playing nations --- Sri Lanka, Bangladesh and Zimbabwe. We should be given credit for that and not criticised."
At 33, Odumbe is very strongly built and exudes the kind of confidence that comes with having seen quite a bit of the world and understanding it well.
He tells you that Kenya does not play first-class cricket as they play only one-day matches.
"For us to get Test status I guess it is important to play the three-day game. I am sure things will fall into place after what we have achieved in this tournament."
He then explains that cricket spread in Kenya first through the colonizers and then through the Asian community.
"My brother (Edward) was the first indigenous player (black) to play for the country but now, more and more blacks are coming into the game.
“It was first a sport played by the upper classes but is now spreading to the middle and even lower classes in some places."
Contrary to what a lot of people believe, the Kenyan national side is not badly paid.
They have a contract with their Board and the players get a monthly salary, reportedly around 40,000 Kenyan shillings plus their match fee. Tusker, a beer-manufacturing unit, is the team's official sponsor.
Odumbe is not willing to reveal what the players actually make but admits, "We do have a sponsor and we are not at all badly off."
Most players in this Kenyan team come from fairly comfortable backgrounds. From families where their parents have either been in government service, like Odumbe's father, or have decent private jobs, like most players of Indian descent.
How does Odumbe see his team's prospects against India in the semi-finals?
"There is something about the Indians that makes us give our best. They have such a strong batting line-up and I guess we want to earn the respect of players like Tendulkar and Ganguly.
“I want to feel that a player like Tendulkar is saying 'this man knows how to bat and play'. As a team, we really perk up when we play India. We go out there to give them a tough time."
Odumbe has, through the sheer weight of his performance, earned the respect of not only the Indians but of the entire cricketing fraternity.
His smashing 98 at Gwalior in 1998 saw Kenya beat India for the first time and even in this World Cup, he has played a couple of classy knocks.
Why is it that the Kenyans do not have a genuine pace attack and rely mostly on slow stuff? Odumbe has an interesting answer.
"Cricket came to us through the Asian community and most of them bowl spin," he says and then, adds, with a smile bordering on the mischievous: "Let me give you an example.”
“You must have heard of Deepak Chudasma (he opened for Kenya). He used to play for a club side called Swami Baba. It was a famous club and they would always shave off the grass from the wicket and make every effort to make the wicket slow whenever they played. So, what can we do?! We all play on slow wickets.''
And this man of many talents, is also a consummate diplomat. And has the art of saying a lot without actually saying it down to a T.
Asked what Sandeep Patil's contribution as coach has been, he replies: "This is a sensitive question and I won't answer."
And then, after being pressed for a more elaborate answer, he finally relents.
Somewhat. "He has done the side a lot of good but not all marriages are smooth.''
Having said that, he also indicates that it is high time he was left alone.