"I come here with my family to carry out my duty towards the revolution. I wish I could carry a rifle, but for me the broom serves the same purpose," said the teacher, adjusting her black veil.
Oreibi said women taking part in the campaign "realise the sensitivity of the current phase" in Libya.
Uncollected rubbish piled up in Tripoli after rebels fighting Kadhafi loyalists stormed the city on August 20, and the capital was plunged in chaos. After Eid al-Fitr, the Muslim feast late last month marking the end of the fasting month of Ramadan, only some sanitation workers returned to their jobs, leaving rubbish and waste piled up in several parts of the capital.
"All that is happening here now is part of a new beginning. Now we feel that we own our country," said Oreibi.
"We want to show the world that we are civilised," she said, wearing black gloves and pointing to a hotel where a large number of foreign journalists are staying.
One of her relatives, Marwa, a 19-year-old engineering student, helps Oreibi, getting compliments and praise from motorists.
"We have to provide something to our country. Before the revolution, we did not have any feelings of nationalism, but now we feel responsible for our country," said Marwa.
"Just like us, journalists should see the beautiful side of Tripoli, where women are not afraid anymore to face problems... they will defend their rights and their country.
A few metres (yards) away, another family member, Abdulhamid Oreibi, 55, a Libyan Airlines pilot and the odd-man out in the women's campaign, gave instructions to youngsters on cleaning the streets.
"We started to love each other more now. For these young people, the future of Libya is clear," he said.
The volunteer work by his wife, daughters and female relatives "is a symbol of women's freedom and dignity in their country, which is no longer ruled by one person," he added, referring to Kadhafi.
The fugitive strongman, his most prominent son Seif al-Islam and intelligence chief Abdullah al-Senussi are all wanted by the International Criminal Court for alleged crimes against humanity.
Volunteers in other parts of the capital show their support by painting revolutionary war murals.
"I am drawing the (green-black-red) revolutionary flag piercing Kadhafi's skull," said Rana Tekli, an 18-year-old foreign languages student busy at a wall near Bab al-Aziziya, the former headquarters of the ousted leader.
"We want to show that we killed him psychologically before anything else," said Tekli, sporting dark sunglasses.
Another painting shows a woman dumping Kadhafi in the "trash bin of history," together with his Green Book of political philosophy, rats and a Nazi flag.
"Now we can smell and breathe freedom," said Tekli's 12-year-old sister, Camilla.