Lt. Gen. William E. Odom, the professorial director of the once-secret National Security Agency, suddenly finds himself and his agency at the center of national attention this week, thanks to the trial of a former NSA technician named Ronald W. Pelton.

Pelton is charged with betraying some of the NSA's most sensitive secrets to the Soviet Union for $35,000. According to the government, he told the Soviets where they were losing communications to the United States and -- probably more important -- about how effectively the NSA is able to interpret and decode the Soviet signals it intercepts.

For the director of the agency -- a massive bureaucracy with a $4 billion annual budget -- Pelton represents the ultimate nightmare. Odom has told acquaintances in recent months that he fears that publicity about Pelton's disclosures might persuade other NSA employes that, since many of the most important secrets have been revealed, they are freer than before to discuss what the agency does.

Odom's concerns about leaks led him to take the initiative this week in the Reagan administration's effort to tell the news media how to cover Pelton's trial. After press accounts of the trial's opening day Tuesday alarmed Odom, he proposed a public warning to the media not to speculate or report additional details about the case. CIA Director William J. Casey also signed the warning, which caused a furor among news executives. But the furor would have been greater if Odom's original draft had survived; he proposed concluding the warning with a threat to prosecute reporters who ignored it.

That Odom finds himself a lieutenant general running an intelligence agency with 50,000 employes is a surprise even to him, according to old friends. Ten years ago he was a lieutenant colonel who doubted that he would ever make full colonel, and was teaching courses on Soviet government and comparative politics at West Point.

Odom's meteoric rise since then was made possible by a professor he knew at Columbia University named Zbigniew Brzezinski, who became President Jimmy Carter's national security affairs adviser in 1977 and drafted Odom as his military assistant. Under Brzezinski's wing, Odom's career flourished in a way reminiscent of Alexander M. Haig Jr., whose service as a military assistant to national security affairs adviser and then secretary of state Henry A. Kissinger in the Nixon White House led to accelerated promotions from colonel to four-star general.

While working for Brzezinski, Odom had a reputation as being a hardliner -- "Zbig's superhawk" is how one former colleague put it. His only formal assignment on the National Security Council staff was "crisis coordinator" and as such Odom was privy to planning responses to the Soviet invasion of Afghanistan and the Iranian capture of the U.S. embassy in Tehran. To reporters, Odom was known at the time as a conduit for news leaks authorized by Brzezinski.

Because of his close working relationship with Brzezinski, Odom also worked on nuclear targeting, civil defense, terrorism and plans for a military rapid deployment force.

Brzezinski, a counselor to Georgetown University's Center for Strategic and International Studies, said in an interview it would be fair to call Odom his "Al Haig."

"Gen. Odom is a top-notch professional. He is the military's top expert on the Soviet Union, and he's also a good tennis player. He would do well in any administration," Brzezinski said.

A native of Cookeville, Tenn., Odom was graduated from West Point in 1954 and quickly began to specialize in Soviet affairs. He studied the Russian language and Soviet area studies and then served as a military attache in Berlin in the mid-'60s, and in Moscow in the early 1970s. His wife, Anne Curtis Odom, is a museum curator. They have a son in college.

One official from the Carter National Security Council staff, who asked not to be identified, said he believed Odom survived and was promoted in the Reagan administration because "his superhawk credentials are beyond reproach." This ex-official remembered Odom as being distrustful of arms control treaties and as champion of a plan to spend $1 billion a year on civil defense. "He had the the idea that a nuclear war with the Soviet Union could be fought and won," the ex-official said.

Another colleague agreed that Odom earned his reputation as a hardliner on the Soviet Union. "But it isn't a knee-jerk reaction. He has studied the issues. There is a depth to his understanding."

Donald P. Gregg, who worked with Odom in the Carter White House and is now national security adviser to Vice President Bush, said yesterday, "I found Bill Odom a very bright, tremendously energetic guy . . . . He comes on strong sometimes. But he knows where the Soviets come from historically. He is steeped in the history of the Bolshevik revolution. He taught it. He saw it firsthand as an attache in Berlin and Moscow . . . . He is a hardline realist, but not a right-wing crazy by any means."

Odom moved to the Pentagon in early 1981 as the No. 2 person in Army intelligence and got the top job, as assistant chief of staff for intelligence, that fall. One official who knew him then described Odom as "a brilliant man. He was extremely bright and quite impressive in esoteric discussions. But he wasn't a good people manager. He was not a real proponent of human intelligence-collection. He was much more interested in technical systems."

This official recalled hearing that Odom once traveled to Europe and told members of an Army counterintelligence unit that technical collection systems were so sophisticated that there was little need for human operatives. "That's not a great way to boost the troops' morale," the official said.

During Odom's tenure as Army intelligence chief there was a controversy about a secret intelligence unit -- the Intelligence Support Activity -- started by his predecessor. Newspaper reports in 1983 said that congressional oversight committees had discovered that ISA had operated without a charter for more than a year. In one case it had given financial aid to an unsuccessful search for missing U.S. soldiers in Laos headed by former Green Beret James (Bo) Gritz without the knowledge of superiors. But one knowledgable Defense Department official said Odom worked quickly to bring ISA under control.

Early last year, while still head of Army intelligence, Odom told the audience at a Washington seminar that the Soviet Union might attempt to ease its disadvantage in technical competition with the United States by trying to negotiate an arms control agreement or increasing trade in strategic materials. President Reagan's Strategic Defense Initiative research program was a challenge of "enormous dimensions" to the Soviets, Odom said.