Brenda Jean Greer spoke quickly and in a very low voice about her infant son yesterday, telling a House Commerce subcommittee about his cleft palate, his missing bones and the ulcers on his eyes.

She blamed his problems on poisons in her yard, and is worried about the new child she carries within her. But the Environmental Protection Agency and local health officials again insisted that no chemical wastes have been found in north Memphis, Tenn., despite four years of tests.

"There is no physical, environmental or medical evidence that identifies a problem in the Frayser community," where Greer lives, said Rebecca Hanmer, EPA administrator in the Atlanta regional office.

Rep. Albert Gore Jr. (D-Tenn.), who chaired the hearing, disagreed. "This is just not satisfactory," he said. "The circumstantial case here is compelling."

Gore called the hearing in the wake of persitent reports of cancers, tumors, breathing problems, rashes and early hysterectomies, often symptoms of toxic chemical exposure, in the Frayser neighborhood of north Memphis.

Six large chemical companies exist within a three-mile radius of the area, and EPA teams are working to decontaminate an old chemical dumpsite on North Hollywood Street 3 1/2 miles away. A reporter for the Memphis Press Scimitar, Leonard Navarro, found 36 cases of cancer in an informal survey of 72 persons in the area.

"I can't see why EPA has not been more responsive to conditions known to exist," said Rep. Ed Jones (D-Tenn.), who represents the Frayser residents.

"It seems to me that our biggest problem at this point is public credibility," said Hanmer.

Tests in the area since 1976 have found traces of chlordane, dieldrin and other chemicals, but nothing that could be called a health hazard, she said.

Hanmer's conclusions were challenged by Joseph Highland, chairman of the toxic chemical program of the Environmental Defense Fund, an organization that first brought the Frayser case to light.

EPA's investigation, Highland said, "can be characterized in large part as incomplete and inaccurate, and it reflects widespread incompetence."

EPA concluded in 1975 when it banned chlordane for all uses except termite control that "there are no safe levels of exposure," Highland said.

Yet measurements in Frayser homes show "several hundred times the background level" of chlordane found nationwide and elsewhere in Memphis, he said. He charged EPA and local health officials with "an inability to understand the toxicological significance of the reported results."

Gore pressed EPA and local officials for a promise to conduct a systematic health survey and to investigate the claims of four Frayser residents that metal drums of unknown substances were dumped and buried at four sites in the mid-1950s.

"I think we would need more substantial evidence that it might be a dumping area," Hanmer replies.

"How are you going to get it if you don't look for it?" Gore shot back.

Hanmer's regional enforcement officer, Sanford Harvey, said county dumpsite records were inadequate, but promised "absolutely" that tests on the alleged dumpsites would be made. Hanmer said she would seek surface soil tests before ordering the deep core samples that might reveal old dumped materials.

Rep. Harold E. Ford (D.-Tenn.), whose district includes the North Hollywood Street abandoned dump, complained that he had heard promises before. He noted that children were still permitted to play around the dump and hogs were raised nearby although dangerous levels of toxic chemicals had already been found there.

There is no money in EPA's budget for health surveys around abandoned dumpsites, said Swep Davis of EPA's hazardous materials office. The agency requested $20 million for it in fiscal 1981 but the amount was cut out at the Office of Management and Budget, he said.

Princess Ray, a mother of six who lives near the Hollywood site, said children from a nearby school play and catch fish in a stream there. "We wonder how many kids attending this school will end up sterile," she said.