Since Sunday, depending on who's doing the talking, this raucous resort town of Maryland's Eastern Shore has either been the victim of a major oil spill or a plot to rob the place of its record-breaking tourist season.

Lately, it's been Ocean City Mayor Harry Kelley Jr. who's been doing the talking. "This is the most ridiculous thing in the world," he said in between intermittent attacks on a constantly ringing telephone. "The Coast Guard has created panic, the Coast Guard is creating chaos. Here I am, the man who calls the shots in this town, whether they like it or not, and I don't know what the're doing."

While the sticky tar-like substance had covered a 100-black stretch of beach and a number of bathers Sunday, the time, tide and beach cleaning equipment had left only a few inconspicuous blobs visible to the thousands of sun worshipers on the beach this morning.

Headlines around the area and some radio reports said something entirely different throughout much of the day, however. Words like "massive" and "most serious" helped turn some tourists around as they planned trips to the seashore.

"We got lucky," said Coast Guard spokesman Lt. Cdr. Randolph DeKroney, explaining the absence of the expected devastation. Nonetheless, the Coast Guard was there along with a mobile command unit, an impressive array of ocean-going and airbone equipment with which to do battle with the enemy and a private beach cleaning company.

What the Coast Guard was doing, at least from its point of view, was monitoring and supervising clean-up of a 10,000 gallon oil slick that arrived on the beaches Sunday afternoon.

While 10,000 gallons of oil is a relatively small amount compared to the 7.5 million gallons that the Liberian tanker Argo Merchant was carrying when she ran aground off Massachusetts last December, it was enough to be "of serious concern," DeKroney said.

According to DeKroney, the oil was a heavy crude oil of the type usually used in then propulsion equipment of large ocean-going ships. It was probably waste oil, DeKroney said, that had been illegally pumped out of the ship's bilges after it had been circulated throughout the engine.

As far as mayor Kelley is concerned, however, he has met the enemy, and it is not the oil. "I can't believe this," Kelley said. "I'm getting calls from Pittsburgh, I'm getting calls from Detroit, they've all heard I closed the beaches. Closed the beaches? Now you know that the oil would have to be up to your belly button before I'd close the beaches."

Early this morning, Kelley said, he had decided "this is stupid. Here I am taking what the Cost Guard says and what the police say and this ain't like Harry Kelley. So I got up in a damned helicopter to see for myself and there isn't any oil. Now I ask you . . .

But the question remained in the air as all four lines on Kelley's telephone lit up. There were Coast Guard officials he had to lecture on what Kelley considered their erroneous reports of the seriousness of the situation.

There were anxious hotel managers to console. There were private contractors offering beach cleaning serives to send off.

There were reporters with the latest rumors to give denials to. But mostly there were dozens of people to reassure like Ron Hess of Hummeltown, Pa., with a wife, a family and an all-important two-week reservation in Ocean City.

"Now Ron," Kelley said, speaking into the telephone and staring heavenward. "This is the mayor of Ocean City talking. No I want you to know that I've been up in a plane and I've gone 10 miles south and 30 miles north and two miles out and I've been up 40th Street and 50th Street and 110th Street and there's nothing there but white sand and people having a good time. Yeah, Ron, I know the Coast Guard is here, they've got a chopper and a cutter and a command post, they've even got a captain down here, they're just going bananas, but you'd be suprised Ron, there's just no oil slick."

It was a lot more peaceful down at the 32-foot-long mobile Coast Guard command center which was inhabited this afternoon by an arsenal of telecommunications equipment, typewriters and one sleepy coast guardsman who had spent the entire night driving it here from Elizabeth City, N.C., with a 21-foot boat attached to the back. "I guess they've got it all figued out now," he said. "They sure don't sound like it last night."

According to Coast Guard officials, 12 cubic yards or two truckloads of oil-contaminated sand have been carted off to a dumping area in nearby Berlind, Md. to be burned. The beach cleaning operation is just about finished.

The Coast Guard, however, is still keeping aerial tabs on a small patch of oil near Rehoboth Beach and on two other patches that were spotted 30 miles north of Ocean City near the Delaware Bay. None of the patches, officials said, is expected to come to shore.

With the immediate effects of the slick in hand, Coast Guard officials said they are now doing some detective work, searching for the ship that caused the slick. According to DeKroney, samples of the dumped oil have been subjected to a complex chemical analysis in order to determine what kind of ship the oil might have come from.

Coast Guard stations from Corpus Christi, Tex., to Portland, Me., he said, have been alerted to board ships that might have been in the Ocean City area at the time of the dumping to compare oil samples with those taken from the slick. A ship found guilty of illegally discharging oil into the ocean, one spokesman said, is subject to civil and criminal penalties, with fines ranging up to $10,000.

Nevertheless, it will probably be some time yet before the culprit ship is discovered, if recent precedent has any bearing. According to Coast Guard Cdr. Jack C. Goldthrope, a Liberian tanker that allegedly dumpted 50,000 gallons of oil into the waters off the Florida keys in July, 1975, was found four months later in the tanker under the Federal Water Pollution Act. of 1st the tanker under the Federal Water Pollution Act. of 1972, he said.

So far, Ocean City hotel managers say that the oil slick and its attendant publicity have caused few reservation cancellations, although some felt that weekend visitors may not show up in quite the same numbers this weekend.

Returning with what passes for tranquility in Ocean City soon, will be one of the more reassuring indications that the beaches here are again safe for vacationers. DeKroney said that he and his family are planning to spend their holiday here next week.