By State Department count, three major and eight lesser wars were going on last week in a world that seemed suddenly beset by blazing battles. Of the three bloodiest encounters, in Lebanon, the South Atlantic and the Persian Gulf, the remarkable thing was the relative impotence if not irrelevance of the United States and the Soviet Union.

Despite the temporary global preoccupation with the dangers of nuclear war, the Israeli invasion of Lebanon, the British-Argentine conflict in the Falkland Islands and the suddenly intensified battle between Iran and Iraq were reminders of the deadly power of conventional weapons.

Despite the preoccupation with Soviet-American confrontation in the traditional core area of Europe, these three major wars and the eight lesser wars on the State Department "watch list" were in the area known as the Third World.

Two of the conflicts involve perhaps the closest allies of the United States.

Yet both Britain and Israel went to war for their own reasons with little consideration of the effects on their U.S. ally, which was expected to give loyal support while suffering in silence the injuries caused to other U.S. relationships and interests.

Reagan administration officials, seeking what solace can be found in the dangerous events, took comfort that the close U.S. allies are winning, and that modern American arms are triumphing in Lebanon, the South Atlantic and the Persian Gulf against Soviet-supplied or European-supplied weaponry. If Britain or Israel were to be threatened with defeat, officials pointed out, far more difficult choices would be forced on the United States.

High stakes are involved for Washington and Moscow and for world order, but the nuclear superpowers have been unable to exercise much power to control events or even to display impressive influence on warring nations with minds of their own.

Even the assembled leadership of the advanced industrial nations, whose just-completed summit meetings were affected by the spreading pall of war, did not seek to intervene because it was clear to all that such efforts would fail.

Underlying the suddenly emerging wars is the unprecedented diffusion of military power to nations throughout the globe.

Advanced weapons, once restricted to a few leading nations, have swelled the arsenals of Argentina, Iran, Iraq, Syria and many other countries. Israel, after acquiring the most highly sophisticated American weaponry, has become an important armorer to the rest of the world. Argentina, on a lesser scale, also has become an arms exporter.

The Arms Control and Disarmament Agency reported that during the decade of the 1970s arms exports to the Third World nearly tripled in volume, even after adjustment for inflation, bringing ever more powerful weapons to nearly every corner of the globe.

Developing countries, formerly armed with obsolete hand-me-downs, accounted for three-fourths of the world's arms trade, including highly advanced missiles, warplanes, ships and other weapons.

Much of the fastest and deadliest weaponry sold in the 1970s is still in the delivery pipeline, and new weapons are entering the pipeline almost without restraint as nations scramble to recoup economic losses by selling arms at a record-breaking pace.

At the same time the ability of leading nations to exert control in other fields has been eroding steadily. The failure in the 1960s of the United States to have its way in faraway Vietnam was an object lesson and a turning point, abroad as well as at home.

The economic crises of the 1970s, especially the quadrupling of world oil prices in 1973 and their doubling again in 1979, drained resources and political resolve in major nations and devastated the non-oil majority of the Third World.

Intensified ideological struggle and resurgent nationalism added to the brew, contributing to the violence and tension of the 1980s. These factors are especially evident in the State Department list of lesser wars: Afghanistan, Kampuchea, Central America, the Spanish Sahara, Namibia, Chad, the Horn of Africa and the two Yemens.

Of the three major wars last week, the two in the Middle East were long in development. Only the conflict in the Falklands, which was touched off by the Argentine military junta's desire to divert attention from internal economic woes, was a surprise to practiced trouble-watchers in intelligence agencies and foreign ministries.

The Israeli invasion of southern Lebanon is a replay on a larger scale of a similar invasion in March-June, 1978, in which the Jewish state tried unsuccessfully to create a Lebanese buffer zone "once and for all."

Israeli military interest in major military action was redoubled when, in April, 1981, Syria placed surface-to-air missiles in the Bekaa Valley after clashes with the Israeli air force.

By this January, U.S. concern about another invasion of Lebanon mounted to the point that President Reagan took it up with Israeli Prime Minister Menachem Begin in a secret letter. Begin, in a five-page reply, promised not to attack unless there was a "clear provocation" from Palestinian or Syrian forces.

Shortly thereafter, on the night of Feb. 1, Begin rejected a proposal for a full-scale invasion of Lebanon presented by its leading advocate, Defense Minister Ariel Sharon.

Begin insisted that such an action should await a more serious provocation than the foiled infiltration that week of a six-man Palestine Liberation Organization team. But the chief of army intelligence, Maj. Gen. Yehoshua Saguy, was dispatched to Washington to serve notice on Secretary of State Alexander M. Haig Jr. that Israel would invade if circumstances seemed to warrant.

By several informed accounts Haig, among all the senior U.S. officials, had been the most urgently concerned for many months about an Israeli invasion of Lebanon. It was Haig who launched the special U.S. emissary, Philip C. Habib, time after time to establish and then maintain a fragile cease-fire.

As recently as May 26 Haig sought to avert an attack by declaring in a Middle East policy speech that Lebanon is "the focal point of danger" for a war of far-reaching consequences. Haig called for "concerted action" in support of Lebanon's territorial integrity and a strengthened central government. He announced that Habib would return again soon with new ideas.

Sharon, who was in the United States at the time, was unimpressed. He told Washington Post editors the following day that Habib is "a very nice fellow," but that his visits had accomplished nothing. In Sharon's view, any PLO terrorism, anywhere in the world, would justify a large-scale Israeli "counterattack."

As it turned out, the trigger for the invasion was pulled by a dissident PLO splinter faction, which reportedly carried out the attempted assassination June 3 of the Israeli ambassador to London, Shlomo Argov. This set off Israeli air raids on Beirut, Palestinian shelling of northern Israel and, finally, the all-out Israeli invasion to remake the map of southern Lebanon.

The Soviet-supplied Syrian missiles were destroyed in the process. But the Soviets, so far, have done little except to communicate urgent concern to Reagan and to condemn Israel and the United States publicly.

The Iraq-Iran war reflects an even longer history of enmity, measurable in centuries rather than decades. It was brought to the newest flash point in September, 1980, by the conclusion of Iraqi leaders that its foe had been weakened by revolution and isolation to the point of complete vulnerability.

A western visitor who was in Moscow at the time recalled a meeting with Boris Ponomarev, the Politburo member responsible for the world communist movement. The Soviet was still indignant at a visit hours earlier from Tareq Aziz, the Iraqi deputy prime minister and second-ranking power, who reported his country's plan to attack Iran and asked for Soviet support. Ponomarev, according to this account, said Moscow would have nothing to do with such a war and condemned it as "adventurism."

Iraq went ahead with the attack anyway. The Soviets recalled two ships en route to deliver routine military supplies for its Iraqi arms client. The Soviets reportedly later allowed some arms to flow to both sides directly or indirectly, but otherwise continued to disapprove of the war.

The United States also disapproved and, despite several entreaties, steadfastly refused to permit U.S.-controlled weapons to go to either side. Nevertheless, there was no shortage of weapons from a variety of countries, East and West, North and South. As the battle flared up anew in recent weeks, Iran has become the winner, becoming, in the view of a senior U.S. official expert, "the strongest and even dominant power in that part of the world."

Of all the blazing battles, the least expected was Argentina's invasion of the Falkland islands and the British counterinvasion from 8,000 miles away. The passions set up by this conflict in the two combatant nations, and in Latin America as a whole, have seemed nearly uncontrollable once the first shot was fired.

The United States, painfully caught between its alliance with the British and its hemispheric alliances and traditional role, proved powerless to head off full-scale battle.

Washington eventually came down on the British side after an internal debate, but continuing uncertainty about its views, as in the case of the celebrated shift of position in the U.N. Security Council June 4, brought angry reactions from all sides.

There was hope for a time that the world would work its way out of the deepening troubles of the '80s through cooperative action by heads of state, especially through the periodic "economic summit" meetings of the industrial democracies that began in Rambouillet, France, in 1975. That hope has faded as the summits have become meetings to limit damage to the alliances and to serve the public relations needs of the participants.

At this point, one-fourth of the way through the decade of the '80s, it is evident that no one nation, nor any one leader, especially in an era of weakened national leadership in many countries, can accomplish a reversal of adverse and dangerous trends.

The diffusion of political power, like the diffusion of military power, continues. Yet, until answers are found, the pestilence of larger and lesser wars, beyond reason or international control, is likely to continue and even to grow.