The upheaval in the poor Himalayan nation was unleashed by a social media ban that was announced last week, but was rolled back after 19 people were killed on Monday as police fired tear gas and rubber bullets to control crowds.
The death toll from the protests had risen to 25 by Wednesday, Nepal's health ministry said, while 633 were injured.
Burnt-out vehicles and twisted metal littered the area around parliament on Wednesday, where army firefighters battled to douse a blaze in the main hall, while the building's exterior was charred after protesters set it ablaze on Tuesday.
TV footage showed youths cleaning up some damaged buildings and clearing debris from roads and the areas near parliament.
"I have been informed by the (parliament) security chief that the fire has destroyed the entire infrastructure. Nothing is left," Ekram Giri, spokesperson for the lower house of parliament, told Reuters from his home in Kathmandu.
Several other government buildings, from the supreme court to ministers' homes, including Oli's private residence, were also set ablaze in the protests, with the unrest subsiding only after the resignation.
Armoured vehicles kept vigil in streets that were largely deserted, with shops and markets shut.
Firefighters were engaged at different locations, while the process of clearing roads was also under way, army spokesman Raja Ram Basnet said.
"We are trying to normalise the situation first. We are committed to protect the life and property of people," Basnet said, adding that prisoners had set Kathmandu's Dilli Bazar Jail on fire before the army controlled the situation.
The main airport in Kathmandu also reopened on Wednesday, an airport spokesperson said, more than 24 hours after flights had been suspended.
In an appeal on X, the army said prohibitory orders imposing a curfew would remain in force until Thursday morning.
"Any demonstrations, vandalism, looting, arson, and attacks on individuals and property in the name of protest will be considered punishable crimes and strict action will be taken by security personnel," the post said.
The army said that relevant parties were co-ordinating to tackle the situation after the protests and resolve the issue.
Media also said preparations were being made for authorities and protesters to hold talks, without giving details.
Former Supreme Court judge Balaram KC urged the protesters to set up a negotiation team, with the army helping to maintain law and order, and called for fresh elections.
"Parliament should be dissolved and fresh elections held," the constitutional expert told Reuters.
"They should discuss forming the next caretaker government."
Most of the protesters were young people voicing frustration at the government's perceived failure to fight corruption and boost economic opportunities, leading to the demonstrations being dubbed the "Gen Z protests".
For years a lack of jobs has driven millions to seek work in countries such as Malaysia, the Middle East and South Korea, mainly on construction sites, so as to send money home.
Wedged between India and China, Nepal has struggled with political and economic instability since protests led to the abolition of its monarchy in 2008.
"It is highly condemnable to kill and injure hundreds without addressing the genuine demands of the youths. This is against the values of the peace-loving Nepali society," King Gyanendra, the last of Nepal's monarchs, said in a statement.
In a post on X, Indian Prime Minister Narendra Modi appealed to Nepal's citizens to maintain peace and order, while Beijing also said it hoped social order and national stability will be restored as soon as possible.
