Defense Secretary Caspar W. Weinberger met in California yesterday with President Reagan, and government sources say the defense chief carried with him two possible options to try to resolve the question of how to modernize the nation's strategic nuclear forces.

One of those options, these sources said, involves a compromise plan, now agreed to by the Air Force and with considerable backing elsewhere in government, that would begin deployment of 100 land-based MX missiles in the West.

The missiles would be shuttled between an initial grouping of 1,000 shelters in a scaled-down version of the "shell game" the Air Force favors as the best way to confuse Soviet targetters and thus try to protect the missiles from being wiped out by Soviet missiles in a first strike. This system eventually might be defended with an antiballistic missile (ABM) defense network.

The second option involves a decision to defer a commitment to deploy the MX, at least for some years, in favor of research and development on other ways to base a new strategic missile and defend it from attack.

This second plan, these sources said, probably would continue research work on the MX, but would push back the need to make a specific decision on deploying it until 1983 or 1984.

In the meantime, research would go ahead to see if a workable ABM could be built to protect a landbased missile, or if a new aircraft could be designed to carry the missile, or if a new so-called common missile could be built that would be considerably different from the MX as it is now known.

In a meeting with reporters Tuesday, the Pentagon's research chief, Richard DeLauer, strongly suggested that he and his boss tend to favor this second option, along with other plans, far more certain, to beef up the rest of the U.S. arsenal with new bombers, submarine-based missiles, improved anti-bomber defenses and command and control systems.

Sources say one attraction of the common missile, which wuld use parts of the Navy's new Trident II missile now being developed and probably parts of the MX, is that it would have considerable financial advantages for an administration hard-pressed to balance its budget, raise military spending and avoid cutting social programs further.

Since this weapon does not exist, much of the costs would be deferred until after the 1983-84 budget crunch the administration is trying to avoid.

Critics argue that the alleged financial advantages are false because they do not include the cost of basing the missile on land and do not answer the question of how to base it on land. That question is at the heart of the dispute that has swirled around the MX for years.

Unless land-based missiles can be made invulnerable to Soviet missiles, an ABM system probably would be needed to defend them. That would add billions to the budget, and probably involve breaking a treaty with Moscow.

Earlier yesterday, Weinberger met in a hotel in Santa Barbara, Calif., with federal budget director David A. Stockman, presidential counselor Edwin Meese III and other officials as the Reagan administration takes another look at the planned $1.5 trillion, five-year Pentagon spending plan to see if some economies can be found.

On his way from that meeting to the helicopter bound for the ranch where Reagan is vacationing, Weinberger would say only "there have been no decisions made yet" on defense budget cuts.

Stockman, asked as he left the staff meeting if some suggested weapons systems may be cut from the budget, said, "I don't think there is any budget in the federal government that can't be squeezed."

"I think he [Weinberger] agrees," Stockman said. "They have done a lot already, and they may have to do more."

White House deputy press secretary Larry Speakes said the staff meeting at the Biltmore Hotel lasted almost four hours, and that decisions on cuts will not be made until next month.

Stockman discounted reports that he has $10 billion to $20 billion in defense budget cuts to suggest, and said only that he was concerned with reducing the entire $44 billion projected deficit.

Some government sources in Washington said they thought any cuts would amount to "a few billion dollars" in the 1983-85 period, rather than much larger cuts advocated by some in the administration.

White House officials have said there has been a dispute within the administration over how much to raise the defense budget, and whether a 7 percent upper limit on annual defense spending increases, beyond inflation, should be based on the last Carter administration budget, as modified by Reagan, or Reagan's first military budget, which is much higher.

Administration officials are sensitive to public criticism of military budget increases combined with cuts in social programs and are seeking what Speakes calls some "savings" in the former area.

Weinberger said yesterday morning that the administration's efforts to balance the budget while raising military spending "depend on how the economic situation comes out," but he emphasized the importance of "rearming American as quickly as possible" to catch up with the Soviets.

Weinberger did not speak to reporters at the Santa Barbara airport when he returned from the ranch and boarded an Air Force plane, reportedly bound for San Francisco.

Meese, after seeing Weinberger off, told reporters that the defense chief had given Reagan "information relating to the options" on the MX but that there was "no real discussion of the system.

Meese said today's meetings were designed to help the Defense Department refine its budget options for further discussion with the president next month. r