''SELL OR DIE,'' exhorts a wall sign in the sales office of Winston Towers, a seven-building condominium complex overlooking the greenstriped surf of upper Miami Beach. ''A reminder to the salesmen,'' said Len Worman, the sales manager, with a chuckle.

Behind the kidding lies a stark reality: In South Florida, the condominium capital of the nation, where individually owned apartments have become a way of life, thousands of new condominiums are going unsold. One estimate puts the number as high as 20,000 - including more than 200 at Winston Towers - and many developers are struggling under a heavy financial burden.

But the developers' plight spells opportunity for buyers, particularly New York-area residents who have long been a mainstay of the Miami real-estate market, just as New York builders and bankers have long been prominent investors in Miami construction. ''Now's the time to make the deal of the decade,'' said William A. Altork, sales director at the exclusive but largely empty Jockey Club III, where only 28 of the 152 units have been sold.

Developers, real-estate brokers and consultants say that not since the last apartment glut and recession of the early 1970's, and probably not in the recent history of the burgeoning Florida realestate market, have builders been so eager to dispose of excess inventory.

Some of the empty units are being offered at 1979 prices. And although developers hesitate to admit it, further discounts often can be negotiated, particularly by customers paying cash. Many developers are offering favorable financing arrangements, and some are even putting unsold units up for auction, accepting bids a third to a half off their original prices.

The result is a variety of attractive deals designed to lure snowbirds looking for a winter refuge, empty-nesters ready to trade a suburban house for a more manageable apartment, and the truly wealthy shopping for a third, fourth or fifth home. Many retirees, by contrast, find even the current terms for condominiums too stiff and relocate instead in lower-priced inland retirement villages.

Housing sales have been depressed across the nation, but the recession's impact on the condominium market in Dade, Broward and Palm Beach Counties on South Florida's eastern shore has been augmented by special factors: a large overstock of apartments left by a formidable surge in construction from 1978 to 1981 and a sharp decline in foreign customers caused by currency fluctuations in Latin America and Europe.

''Nobody in this town is doing any business,'' said Ron Lavan, chief executive officer of the Muss Organization, whose deluxe Quayside development has not escaped the travails of lesser projects.

Only two weeks ago, an additional uncertainty was added when rioting broke out in the Overtown section of Miami. Although the neighborhood is miles from tourist and recreation areas near the beach, the disturbances, set off by the killing of a young man by a policeman, underlined the social tensions in the fast-growing metropolis.

One indication of the state of the market can be found at Turnberry Isle in North Miami Beach, perhaps the Miami area's choicest address, where residents, hotel guests and yachtsmen rub shoulders with such celebrity-owners as Jimmy Connors, John McEnroe and James Caan. Some apartments that once sold for up to $325 a square foot are down to $180 a square foot, said George Berlin, the project manager. That still adds up to nearly $350,000 for a 1,900-square-foot, two-bedroom apartment, but relatively speaking, it is a bargain.

Across town, at the similarly luxurious Grove Isle, bedecked with art works by Alexander Calder, George Segal, Isamu Noguchi and others, about a third of the 510 units remain available. ''We're making deals,'' said Martin Margulies, considered one of Miami's most financially secure developers.

At the other end of the price scale, yet within sight of Turnberry, is the largely empty Delvista Towers, where a 16th-floor one-bedroom apartment with an alcove convertible to a second bedroom is for sale at $87,000, with a 5 percent discount for cash customers. A nearby project called Waterview offers similar deals.

Beyond lowering their prices, developers have devised some innovative strategies to attract buyers. One device used increasingly is the real-estate auction, in which vacant lower-priced apartments are sold to the highest bidder, although with some limitations.

While some developers disdain the practice as declasse, others, including buyers, praise it as productive. ''I'm more than delighted,'' said Ruth Boyd, who last June bought a two-bedroom condominium in Fort Lauderdale for $52,000 - $37,000 less than what a similar unit there sold for in the inflated market of 1980.

Meanwhile, developers who insist they would never stoop to putting their high-priced units on the auction block are competing with amenity packages, celebrity rosters, security systems and private clubs - ''snob appeal, to be blatantly frank,'' said Mr. Altork of Jockey Club III.