Leon Levy and his partners say they don't want to take over Trans World Corp., they just want the present management to break it up and spin off all its components.

Levy's group, known as Odyssey Partners, says the five main parts of Trans World, including TWA Airlines and Century 21 Real Estate, would be worth far more as independent companies than they are asparts of a conglomerate, and they are asking the company's stockholders to demand a divestiture plan from Trans World's management.

Their proposal is on the agenda for the company's annual meeting April 27. Trans World lost a court battle to keep Odyssey from obtaining its stockholders list for a proxy fight, and now both sides are campaigning for stockholder support and denouncing each other in full-page newspaper advertisements.

The Odyssey Partners are Levy, Jack Nash and Lester Pollack, the former owners of the Oppenheimer investment and mutual fund group. When they sold Oppenheimer to a British firm last year for $162.5 million, they received $117 million in cash, and they invested about $10 million in Trans World stock. They say their stake would be worth a lot more if Trans World would break itself up.

Trans World consists of five divisions: TWA; Century 21; Hilton International Hotels, including the Vista chain in the United States; the Canteen food-vending service; and Spartan Foods System, which operates Quincy's Family Steakhouse restaurants and many Hardee's fast-food outlets.

For 1982, the company reported revenue of $5.1 billion and net income of $29.9 million, down sharply from a $61.6 million profit the year before. The airline division lost $44.5 million, wiping out the profits made by all the other divisions.

"We began with the idea that the parts of a company are usually worth much more than the whole," Levy said. "There's a good body of opinion saying it's difficult to run five different totally unrelated businesses, and somebody who wants to own Century 21 or a hotel company may not want to own an airline." He said management should consider breaking up the company into its five parts, with shareholders receiving stock in all five proportionate to their shares in the parent and free to choose whether to alter the portfolio.

According to Odyssey's proxy statement, the "separation value" of Hilton International alone would be $1 billion, greater than the total value at current prices of all Trans World's outstanding stock. Based on a study by the consulting firm of Booz Allen & Hamilton, Odyssey calculated that a share of Trans World worth about $33 today would be worth up to $70 if the company were dismembered.

Trans World's management, led by Chairman L. Edwin Smart, has not specifically refuted Odyssey's figures. The company is asking stockholders to consider whether Odyssey "is sincere in its proposal, or whether its main interest is to reap short-term speculative profits by promoting a scheme that has increased speculative interest in Trans World's stock."

Diversification is a strength, not a weakness, because the company "used to be totally vulnerable to the cyclical volatility of the airline business" but now has a "growing and stable base of earnings," Trans World argues.

Although Odyssey disclaims any intention of trying to dislodge the present Trans World management, Smart and other senior officers have protected themselves against such a move with "golden parachute" contracts. The contracts, signed in December, would give the six top executives salary and stock worth more than $8 million if a new management unseated them within two years of a takeover.