Northern Virginia fuel oil companies struggled against ice and snow and exhaustion last week to keep up with an increased demand for heating oil which left some customers temporarily with empty tanks.

Strategies for meeting demand included massive overtime, delivery to isolated houses by four-wheel drive jeep and dragging hundreds of feet of fuel oil hose up icy driveways that stymied trucks. Most of the time these efforts were successful, said fuel oil company spokesmen. Even so, most of those queried conceded that a few contract customers ran out before refill.

Even harder to meet was demand from customers who do not have regular delivery who called looking for oil, they said.

"We have to deliver to contract customers in good times and bad times," said Bill Murphy of Vienna Fuel, who said about 99 per cent of Vienna's business is automatic deliveries. "If you're a will-call customer and we can't handle you, we'll tell you so you can make another arrangement."

To make sure that automatic delivery customers don't run out, Murphy said Vienna delivery men had been working weekends and relying on chains and a jeep to get them to relatively isolated homes. "The cold weather hasn't affected us as much as the snow," he said. If a truck can't get near enough to a home to deliver, Vienna sends in the jeep with 30 or 40 gallons - "enough to hold them till we can get a truck in," he said.

For at least one customer, a nursing home, he sends in fuel a few days in advance of anticipated need, he said. "With them, you can't take the chance," he said.

"You just have to go slower and be much more careful," said Bill Best, general manager of the Fairfax Fuel Company. Fairfax was in excellent shape for deliveries before the snow, which made it harder to keep up, he said.In a normal year, the company seldom has as many as half a dozen run-outs with contract customers, he said. "In the last week we've had two that I can think of," he said.

Besides the snow and ice, fuel companies were facing more rapid consumption than usual. During the first 13 days of the year cumulative temperatures were 107 degrees below the total normal temperatures would have produced, with a predictable effect on fuel consumption.

Most fuel oil companies base their automatic deliveries on a formula that includes the customer's historic rate of consumption and the number of "degree days" that have passed since the last delivery. Degree days are the number of degrees between the daily temperature and 65 degrees - the industry standard for what it should be inside.

In the first 12 days of 1977, degree days were running 42 per cent higher than normal.

"We're working longer and harder trying to keep up," said a company spokesman for the Robert Shreve Company. "It's like waging a war - you've got to hang in there," he said. The spokesman said the company had worked Sunday before last anticipating more cold weather and had not had any more run-outs than usual so far. "They're calling for a break in the weather, thank goodness," he said.

"We're keeping up, but we're keeping kind of busy," said Dorothy Soter, office manager for Franconia Fuel. Franconia uses farmers as drivers, she said, and they have been working overtime, Saturdays and Sundays.

Mike Neish, a tractor-trailer driver for Thomas J. Fannin and Sons, said the firm's tractor-trailers were running 24 hours a day bringing in fuel from area terminals - "wherever we can get it at the cheapest price." (Fuel oil is selling for about 45 cents a gallon in the Washington area now, compared to about 42 cents a gallon last year.)

"I'm driving more than I would like to," said Neish.