Rescue workers, stalled for two days by fog and mud, today fought their way through uprooted trees and debris trying to reach hundreds of residents stranded by northern California's winter storm.

The violent rainstorm has killed at least 24 people, forced the closing of the Golden Gate Bridge and caused an estimated $100 million in damage.

In Sacramento, Gov. Edmund G. Brown Jr. announced that he was asking President Reagan to declare a major disaster in the counties of Contra Costa, Marin, San Mateo, Santa Cruz, Sonoma and Humboldt. If Reagan grants the disaster relief, as expected, the counties would be able to receive wide-ranging federal assistance, such as relatively low-interest loans for homeowners and businesses, temporary housing for victims, cash grants and tax advice.

Up to 20 people were trapped when a mountainside collapsed at 2 a.m. Monday and washed over 300 acres of expensive homes in this wooded Santa Cruz County community about 60 miles south of San Francisco, witnesses said. One body has been found, and rescue teams expect to find more.

Earl Robertson, spokesman for the rescue effort, was asked if there was any hope for residents caught in the slide. "If there's anybody in there--no," he replied.

Ten miles south of San Francisco in Pacifica, the body of 9-year-old Billy Velez was recovered from the rubble where the bodies of his sisters, Michelle, 13, and Melissa, 4, were found eight hours earlier. The sleeping children were killed Monday night as a house above theirs on a hillside collapsed in a mudslide, crashing into their own.

North of San Francisco in Marin County, where 80 homes were leveled by mudslides and another 150 were damaged, officials feared a slide had undermined U.S. 101, the road to the Golden Gate Bridge.

The bridge, which links the county with San Francisco, was closed because of the worries about Highway 101. The mudslide Tuesday night toppled two homes down a hillside in the fashionable community of Sausalito, killing one person and forcing the evacuation of 800 people in an area three blocks wide and a half-mile long.

Before this week, the suspension bridge had been closed only once, according to the Golden Gate Bridge District. The bridge shut down for five hours Tuesday because a slide blocked U.S. 101. The debris was cleaned up just hours before the newest slide closed the span again.

In Ben Lomond, officials were awaiting the arrival of heavy equipment while two 10-man crews worked with chain saws and shovels. A slide closed the main road into the area and the only access to the valley was by foot. Reporters trying to hike in were threatened with arrest.

"We believe there are six or seven homes buried in the slide," said Assistant Fire Chief Wayne Drager. "There may be more that we can't even see. We'll know where to dig for the ones we can see, but we still don't know how much is there."

The National Guard trucked in water after supplies here were contaminated in the storm. The city of Santa Cruz was running low on water and officials urged residents to limit use.

Elsewhere in hard-hit Santa Cruz County, 70,000 homes and businesses were still without power after 36 hours, and utility spokesmen said power would remain out for at least another 12 hours.

Deputy press secretary Larry Speakes said Reagan was being kept informed of the extent of the storm damage by presidential counselor Edwin Meese III, who was in contact with the Federal Emergency Management Agency.

Bob Blair, a FEMA spokesman, said Brown's request for aid was not received until after the close of business today and would be processed and evaluated starting Thursday.

Speakes said that among the federal agencies standing by to help were the U.S. 6th Army, the Army Corps of Engineers, Federal Highway Administration, Small Business Administration, Veterans Administration, Social Security Administration, the Internal Revenue Service and the Department of Agriculture.