His experience, like that of the other traders in this market area, where several hundred people were caught up in rioting last week, provides a salutary warning that Nigeria's much-heralded shift to civilian rule is in danger of going off the rails - although through no fault of the President, Olusegun Obasanjo.
The reports at the time of the riots, around 26 November, were sketchy: more than 40 people were thought to have died in street fighting between two ethnic groups - the Yorubas, who dominate in the south-west, and the Hausas, from the north.
On the face of it, these were classic marketplace rivalries. But it soon became clear that the death toll - in brutal necklacings and machete attacks - had exceeded 100. The government did not hesitate: security forces were ordered to shoot troublemakers "on sight" and an 8pm to 6am curfew was imposed. It is still in force.
As any Lagosian can confirm, Mr Odirah is Igbo - by tradition the tribe of car spares dealers in Mile 12. "Many of the Igbos are leaving Lagos and going back east. At the very least, we are sending our wives and children. We believe that when the Yorubas have finished with the Hausas, they will go for us," he said.
In Africa's most populous country, this is the tribal nightmare that everybody feared - resonant of the 1967 Biafran secessionist war, in which more than one million people died. That war, in which easterners demanded autonomy, gave the military a pretext to takeover and rule almost uninterruptedly for the next 32 years. The 200 ethnic groups of Nigeria, said the soldiers, were not capable of cohabiting, other than at the end of a gun barrel.
Mr Odirah blamed the Oodua People's Congress (OPC), an extremist Yoruba organisation which, he said, wanted to secede from Nigeria. "The OPC will stop at nothing," he said. "What I saw was pure carnage - people being hacked and shot and burnt. I saw maybe 200 corpses in the street in front of my shop."
Even 10 days after the riots, the slum remains littered with burnt-out cars and minibuses. Behind the traders' stalls and shacks which line the roads of Mile 12 and adjacent Ketu, breeze-block homes have been burnt or had their iron roofs ripped off.
"We're all terrified. The police presence seems minimal and there are rumours of a Hausa retaliation. None of our customers will come here any more," said Mr Odirah.
Across the highway, in a Hausa sector of the huge market area, Sarki (Chief) Jibril Usman pleads for calm. "There is a dispute between Hausas and Yorubas over the market chairmanship, but it is not the first, and we have always resolved these arguments amicably in the past.
"What these Ooduas do is to seek out areas of friction and bring their violence. We did not know any of the area boys [hooligans] who did the killing last week. They were from outside. It mystifies me. Hausas and Yorubas cohabited here for years. We even intermarried," said the Hausa chief, in his 70s.
Chief Usman, whose subjects are mainly vegetable and livestock sellers, said he knew the rioters were from the OPC because they wore the Yoruba nationalist group's badges and T-shirts. Armed retaliation by Hausas, he said, was unthinkable. "We are businessmen, not rioters."
For their part, the OPC deny any role in the fighting and claim that President Obasanjo's order to shoot on sight has led to five deaths among their members since the riots. "They were shot dead by police in their homes in Ketu. The President's order is undemocratic and reminiscent of military rule. It could lead to genocide," said Frederic Fasheun, the group's president.
Confusion, denials and conspiracy theories abound. This, say observers, is precisely what Nigeria's enemies of democracy want to achieve. Reports of more than 1,000 deaths in ethnic conflict since President Obasanjo took office at the end of May only increase the feeling of insecurity. Clashes between tribes in oil-rich Delta state, and kidnappings of oil workers, are now so common that they often do not make the news. Yet Nigeria's post-military government is doing well, and most people are enthusiastic about the changes they have seen.
The petrol queues have gone all over the country. Electricity, for those who have it, is cut off less often.The government of one of the world's leading oil exporters, helped by the increase in prices, is even talking of spending more on health and education. Some foreign investors are tiptoeing in.
But the danger, say observers, is that President Obasanjo's drive against corruption - the move for which he has been praised in the rest of the world - will backfire. The ethnic fighting, according to one diplomat, could be "their way of telling the new government to leave them alone".