The D.C. statehood convention, after three months of often stormy debate, gave final and overwhelming approval yesterday to an 18,000-word constitution as the foundation for the District of Columbia's uphill bid to become the state of "New Columbia."

Setting aside the feuds and disagreements that had racked much of the convention, the delegates broke into cheers and hugged one another when convention secretary William Cooper announced the vote around 3 p.m.: 37 for, two against and four abstentions.

The mammoth document, longer than the constitutions of many existing states, would establish most of what is now the District of Columbia as the 51st state. The state would have a governor and a lieutenant governor, a 40-member unicameral legislature called the House of Delegates, a two-tiered court system, full budget and taxing authority, new election procedures and the power to create semi-autonomous neighborhoods within the city-state.

The document also contains a sweeping bill of rights and tax and labor provisions that alarmed some delegates who opposed passage of a document with unorthodox components that might lead to rejection on Capitol Hill.

The constitution, for example, gives government workers, including police and firefighters, the right to strike and guarantees the right to a state-supported job or income for all residents. It prohibits retail taxes on groceries, drugs and other medicines, expands the rights of criminal suspects, and abolishes congressionallybestowed property tax exemptions for organizations such as the National Geographic Society and the Daughters of the American Revolution.

With the convention now over, the battle begins to gain approval of the constitution, first among city voters and then in Congress. It is likely to renew debate over fundamental concepts of self-determination for the city--concepts that have largely lain dormant since the District of Columbia obtained limited home rule in 1975 and, more recently, since the drive for full voting rights in Congress lost momentum.

Under a bill currently before the D.C. City Council, the constitution adopted yesterday would go on the ballot in the Nov. 2 general election. If approved there, it would then be sent to Congress for consideration. Upon approval by a simple majority of both the House and Senate, statehood could be implemented.

Several key members of Congress, however, have said there is little sentiment on Capitol Hill for statehood, and the constitution--especially with its unorthodox bill of rights and other provisions--may face a hostile reception.

Most convention delegates ignored urgings by some colleagues to keep the document simple and "unpolitical." Speaker after speaker yesterday at convention headquarters in the old Pepco building at 10th and E streets NW praised the new constitution as the embodiment of their aspirations and of those of the voters who elected the 45 delegates last year to write the document.

Ward 4 delegate Victoria Street called it a "bold document."

"It takes courage to dare to be different," said at-large delegate Barbara Lett Simmons.

It guarantees "freedom and sovereignty in New Columbia," said Ward 1 delegate Anita Shelton.

But other delegates voiced reservations about the constitution and skepticism about its chances of surviving city voters or Congress.

"It is a Christmas tree of political innovations," said Ward 3 delegate Joel Garner in a statement submitted to the convention. Garner was one of two delegates absent yesterday. "I cannot support . . . the constitutional provisions adopted by this convention," he said.

"This document actually harms our society," said Ward 3 delegate Courts Oulahan.

Ward 7 delegate William Blount called it a "B-plus constitution."

In the final vote, the only two delegates who voted against adoption were Oulahan, an attorney, and fellow Ward 3 delegate Gloria Corn, a French-language researcher and political consultant. Both are Republicans.

The four delegates who abstained were Sandra Ford Johnson, a D.C. school administrator from Ward 7; Brian P. Moore, an unemployed health adminstrator from Ward 2; Kenneth Rothschild, a taxi driver and housing activist from Ward 2, and Philip Schrag, a law professor from Ward 3.

The constitution adopted yesterday not only defines in detail the structure of the proposed new government, but also contains several social policy statements--manifestos for the health, education and security of the new state's population.

"It is the responsibility of the State to protect, restore and enhance the quality of the human environment for this and future generations," says one section.

" . . . The State is committed in its educational goals to the preservation of cultural integrity and to the promotion of equality of opportunity for every individual to develop fully," says another.

But there are plenty of nuts-and-bolts sections as well.

The constitution specifies, for example, that the 40 members of the House of Delegates would serve four-year terms. All would be elected from single-member districts, with no at-large members.

Under the new constitution, the governor and the House of Delegates would retain essentially the same relationship as the mayor and City Council do now.

The governor would serve a four-year term--as does the mayor now--and run on a slate with his lieutenant governor. The governor and lieutenant governor could serve a maximum of two consecutive terms.

The judiciary article of the constitution provides for a nine-member Supreme Court and a 44-member Superior (or trial) Court--the same composition as the present D.C. Court of Appeals and D.C. Superior Court.

The article also empowers the legislature to create an intermediate appellate court and other unspecified "inferior" courts, such as neighborhood tribunals for hearing domestic disputes.

The intermediate appellate court provision was added late in the convention after several delegates argued that the proposed State Supreme Court--which must hear all cases en banc, or as a group--might become overwhelmed with the caseload.

The present D.C. Court of Appeals hears most cases in panels of three judges each. Even so, court officials say they are jammed with an enormous backlog of cases.

A new feature under the constitution is that all judges, after being appointed by the governor, would be subject to "retention elections" by city voters every six or 10 years, depending on the judgeship.

Other major features of the proposed constitution include:

* Creation of a nine-member state board of education with eight members elected from local districts. The ninth would be a high school student elected by fellow students. School attendance would be compulsory through age 18, not 16 as currently required.

* Empowerment of neighborhoods and other local areas within the city to incorporate themselves as separate government entities with limited authority to provide public services.

* Establishment of boundaries for the new state. The external boundaries would be the same as the present District of Columbia, but a small federal enclave would be carved out downtown, including the Capitol, House and Senate office buildings, Supreme Court, Library of Congress, Federal Triangle, the Mall and the White House.