Virtually unrelieved gloom characterizes the spirit marking the observation here of the shah of Iran's 59th birthday this week. Demonstrations and strikes against the regime continue to sweep the country.

Though martial law has been declared, it only serves to underline the distinct limitation of using military force against popular discontent. The best option available to the shah seems to be an experiment at liberalization, which is at once out of tune with his spirit and very dubious as to the end result.

For those not actually in this country, it is hard to realize how a once secure scene has been swept by turbulence. There are daily demonstrations against the shah in every corner of the land. The tone of the protests is harsh. A student rally that I witnessed at the University of Tehran demanded "death to the shah." One of the placards set as an objective "a republic of the people of Iran led by the working class."

More damaging than the demonstrations are the strikes. They started in the banks, spread to the civil service and are now tying up every part of public and private industry. The government has already conceded about $4 billion in wage increases for the next six months alone. One calculation is that during the next year a tenth of the national budget will go to higher pay for government workers.

The loss in services is incalculable. The telephone works only intermittently. Mail has gone undelivered for weeks. Rumors of a strike by gasoline dealers, which turned out to be false, caused a near panic here the other day.

Many of the strikes, moreover, have distinct political implications. The oil-company workers insisted, for a while, on the ouster of the oil minister. The workers at one big bank refused to go back to their jobs unless pictures of the shah and his family were taken down from the walls.

perhaps the most notable feature of the continuing trouble is the inability of the forces of law and order to do their thing. The martial law that now applies to a dozen cities, including Tehran, authorizes the soldiers to break up any gathering of more than three people.

But the troops stood by and watched the demonstration that I witnessed at the University of Tehran. One general officer remarked to me that a military reaction would have provoked a worse counterreaction. The day after the demonstration, the government declared that in the future the soldiers would not even go onto the university campus.

That concession is typical of the policy now being followed by the shah and his most recent prime minister, Shaarif Imami. The government is easing up on censorship, releasing prisoners and jettisoning right and left the development projects opposed by the religious leaders who touched off the present wave of protests.

The hope is that the concessions will calm the disorder enough to permit elections in the spring. The new government would presumably work out a rearrangement of power with the shah. While determined to maintain his dynasty, and to turn over the throne to his son and heir, the shah seems ready to accept a constitutional monarchy. "It's okay with me," he told one visitor.

But he showed no enthusiasm for that outcome, or even hope. He shrugs his shoulders when asked what he thinks will happen next. He shakes his head when asked if his allies can help. The trouble with that gloomy attitude is that there is one distinctly bad outcome only the shah can avert.

Though loyal to the monarchy, the military is growing distinctly restive under the current restraints. "We are handcuffed," one high-ranking officer told me. So unless the shah actively restrains them, the soldiers are apt to take matters into their own hands with results incalculable to this country, the Persian Gulf, and all the areas - including Europe, Japan and the United States - that depend on oil from the gulf.