The dark rings around Dariya Bilichenko’s eyes betray fatigue. After enduring two weeks of constant artillery shelling, she took her 3-year-old daughter and joined a convoy of passenger vehicles on 28 January to flee the railroad town of Vuhlehirsk.

“The shelling worked like clockwork, from 8 a.m. to 4 p.m. While they fought, we hid in the cellar,” Mrs. Bilichenko says. “They specifically targeted residential areas.”

By the time Russian tanks had rumbled in on the heels of retreating Ukrainian government troops, just days later, Vuhlehirsk was leveled. From a prewar population of 10,000, only about 3,000 people remain, according to the United Nations Office for the Coordination of Humanitarian Affairs.

“My mother-in-law’s house was completely destroyed,” adds the 22-year-old, whose husband stayed behind to prevent their one-bedroom house from being confiscated by separatists, a common occurrence with abandoned homes.

Her flight to safety was harrowing. The driver of the car in which she escaped was shot in the leg trying to get through a strategic transport hub. Their convoy had to dodge rocket salvos when turning back along a detour through separatist-held territory.

After traversing five cities, Dariya Bilichenko finally joined a dozen distant relatives on 20 February in government-controlled Sviatohirsk, not far from a monastery situated where the eastern Luhansk, Donetsk and Kharkiv regions meet.

Her odyssey was over. But the memory haunts her.

“She screams in her sleep, she repeatedly yells to hide and take cover,” says family member Iryna Shvedenko, the 54-year-old matriarch of the extended family, who fled her home in the town of Yenakieve in late July 2014.

Although Mrs. Bilichenko’s screaming spells happen less frequently now, she feels compelled to drop to the floor when hearing a loud sound, “even if I hear a stiff knock on the door.”

Stories such as hers are all too common in war-weary Ukraine, where Russian-backed separatists in the eastern portion of the country have taken on the Ukrainian authorities and its army. But where there is fatigue and trauma, there is also help. In early March, an aid worker of the Catholic Church registered Mrs. Bilichenko to receive $300 in financial assistance.

It is just one component of the numerous outreach programs for expelled families and individuals being implemented under the auspices of Caritas Ukraine, a network of charitable groups structured through local parishes and jurisdictions of Ukraine’s Catholic churches. In Ukraine, the main driver is the Greek Catholic Church and its 5.5 million faithful. Bolstered with international funding from charities such as CNEWA and Catholic Relief Services, Caritas is the second-largest social charitable organization — after the Red Cross — working on a grass-roots level with the country’s displaced people.

For people such as Dariya Bilichenko, Caritas is providing more than just financial help. It is also providing them with a more elusive gift: hope.

At one point last summer, 26 displaced people occupied three bedrooms and a living room in the one-level house in Sviatohirsk. Many slept in their cars or outdoors.

Iryna Shvedenko and her husband arrived first with the blessing of the home’s owner, a distant relative who lives in neighboring Russia. Her two daughters followed less than a month later: Kseniya Stulova and her three school-aged children, and Anastasiya Stulova with two children, ages 5 and 1.

Kseniya’s 9-year-old son and 11-year-old daughter are taught at home using textbooks borrowed from other families because the local school is overcrowded. More than 5,000 displaced people live in the area, which includes neighboring Slovyansk, the Sviatohirsk Monastery and a convent in nearby Bohorodychne.

Just before winter, the household received three installments of 4,700 hryvnia (about $214) from Caritas Ukraine to purchase what they needed. Rent is free, but they have to cover heating and electricity expenses, and feed seven children.

By late February, 9,600 internally displaced people had received assistance for the winter, according to Caritas Ukraine. The $1.5 million emergency aid program allows vulnerable recipients to choose what they buy — whether insulation for windows, firewood, blankets or boots — often without showing proof of purchase.

“We especially target the vulnerable,” says Petro Matiaszek, an American who advises Caritas Ukraine on emergency responses. “That includes people with chronic illness, age, multiple children, those living with disabilities and low income.”

The Caritas program meets a crucial need. Many who fled before the onset of winter often took little money and few belongings, believing the war between the Ukrainian government and Russian-backed separatist forces would not last long.

The Stulova sisters brought only a bag of summer clothes with them.

About 25 miles to the north in Izyum, Yelena and Oleksandr Zavizin of Horlivka took their young daughter and son, along with some money and clothing on 27 June, when they got on a volunteer-operated bus headed for the Kharkiv region.

Ukrainian forces were on the offensive then, winning back territory that separatists had taken in April 2014, when armed uprisings spread throughout the nation’s two easternmost regions of Luhansk and Donetsk. Ukraine had already lost the Crimean peninsula and its 2.7 million residents in March to Russia. Horlivka, a city of 272,000 before the war — now 180,000 — faced shelling, according to the United Nations.

“It was the incessant fire that made us leave,” explains Mr. Zavizin.

So the couple headed to Izyum — then the Ukrainian military’s eastern headquarters on the front line — where they stayed with their aunt for two months before finding a tiny, 150-square-foot home to rent for $23 on 1 September. Caritas helped the Zavizins pay for rent, and to purchase firewood and an air mattress.

“It’s quiet here. I love the surrounding forest,” Mr. Zavizin says. “I can live here; there’s no shelling.”

The number of refugees in Izyum has swelled. There were 1,700 displaced families living in the area in June; now there are 20,000, according to an advisor to Caritas, Denis Davidov of Catholic Relief Services.

Barbara Manzi, head of the United Nation’s humanitarian affairs office in Ukraine, says many fled with few belongings. “When people see danger coming, they flee. They have no time to organize, to grab what they think is needed. The hope is to return soon.”

The United Nations has registered 1.1 million Ukrainians as internally displaced; most of those uprooted from their homes, approximately 700,000, now live in the five easternmost regions of the country: Dnipropetrovsk, Donetsk, Kharkiv, Luhansk and Zaporizhia.

U.N. sources also cite that the war has claimed more than 6,000 lives since last April, including 63 children. An estimated 2.2 million people still live in conflict-affected areas, where they face indiscriminate shelling and limited access to basic services.

“Five million people across the country are now in need of humanitarian assistance,” said John Ging, OCHA operations director, to the U.N. Security Council on 6 March.

“Approximately 1.4 million people have no access to health care. Those remaining in conflict-affected areas, particularly in densely populated urban areas, face ongoing security threats due to military activities. Lives have been lost, basic life-saving services have been disrupted, access to banking and cash services are limited, food and non-food items are increasingly scarce and expensive, and there’s been an upsurge in lawlessness across the country.”

In November, the Ukrainian government in Kiev exacerbated the situation for the displaced by cutting pension payments and halting banking operations in the occupied east. The controversial move, defended by the government as a way to prevent money from falling into the hands of the rebels, irritated the separatist authorities. Some agencies, including the United Nations, have called on the government to resume financial disbursements.

“It’s a major crisis. People lack the means to survive in the non-government controlled area,” says Barbara Manzi. “Trust is difficult between Kiev and the regional governments and population in general.”

The government continues supplying electricity and gas to separatist areas. Still, with its economy teetering, Ukraine cannot address the needs of its refugees alone. That is where aid groups, such as Caritas, the Red Cross, the Knights of Columbus and organizations of the United Nations, have stepped in to provide immediate relief, including shelter, access to food and basic medicine, and counseling to deal with physical and psychological trauma.

The latter’s effect cannot be underestimated, explains Ms. Manzi, drawing upon 16 years of experience in conflict zones, including service missions in Baghdad.

“The level of trauma is immense,” she says. “Because of the violence, step by step, penny by penny, everything is gone. I’ve seen elderly people whose eyes are lost; they look empty with no more energy.” Nevertheless, she marvels at their resilience. “There still is kindness, love and solidarity.”

One such person is Lidia Usypenko, a 67-year-old pensioner from Donetsk — a refugee trying to adapt to life in Slovyansk.

When asked what is most difficult for her, she says bluntly: “Daily life. Everything here, in the apartment, is alien to me. I can’t touch the silverware, flatware, dishes, even drink out of the coffee cup.”

Caritas provided her with support for the chemotherapy that treats her breast cancer. A former chief of personnel at a Donetsk coalmine, she has lived in a one-bedroom apartment with her 27-year-old daughter since October. Mrs. Usypenko sleeps on a fold out couch with no mattress covers and complains about water constantly leaking in the pipes of the kitchen and bathroom.

“I sleep like a bum,” she says.

She has had to flee twice. The first time was 21 July, when shrapnel struck her windows in Donetsk. “The constant stress, I couldn’t take it,” she explains. She took flight again in August from the Azov Sea coastal town of Novoazovsk, when pro-Russian forces took the city in a counteroffensive.

“We lived normally. Why did this start, what caused the war?” she asks rhetorically. “I don’t know how to describe it. It’s pointless, mindless and inhumane — it is a crime against God for brother to shoot brother.”

At the Caritas office in Kiev, help from the Knights of Columbus comes in the form of $25,000 to provide foods with long shelf lives to refugees. Only two weeks into the project, more than 800 people, or 200-300 families, have received assistance, according to financial secretary Serhiy Zahlotsky.

More than 80,000 displaced people moved to the Kiev region, according to United Nations data.

Iryna Pukhnyak, youth outreach manager for Caritas in Kiev, said that visitors are welcome to other services, which include free laundry facilities, psychological and spiritual assistance, clothing delivered from Germany and elsewhere, hygienic and sanitary products, and a soup kitchen that can feed 100 people.

At the parish level, the church helps refugees find places to live through parishioners wishing to take in roommates or residents, says the Rev. Oleh Panchynyak, head of the Ukrainian Greek Catholic Church’s information department.

Volunteers help the elderly, arrange for donations of medicine, wheelchairs — “whatever they need,” the priest says.

Father Panchynyak says that with the influx of internally displaced people, the value of psychological counseling is abundantly clear.

“We clergymen have received renewed training on how to speak to displaced people, what topics to avoid, and which topics to cover, but unfortunately people don’t yet see the value of speaking to psychologists or to priests who can act in that role,” says Father Panchynyak, explaining that psychology in the Soviet era was politically abused to imprison dissidents and other enemies of the state.

In Dnipropetrovsk, where the United Nations says there are more than 70,000 displaced people, the Rev. Vasyl Panteliuk, Donetsk Caritas chief, says that the war is testing humanity.

“It tests who you are. It tests you as a person, as a Christian — those who were bad, became worse, those who were good, became better,” he says.

“Political views don’t matter, what matters is how we, step-by-step, improve the nation.”

Mark Raczkiewycz is editor at large for the Kyiv Post in Ukraine. His work has appeared in the The Financial Times, The Irish Times and Jane’s Intelligence, among other places.