Two major issues for the District of Columbia are likely to be resolved in the final day or two of Congress before adjournment, now slated for this week.

One would correct deficiencies in the city's home rule charter that arose out of a Supreme Court decision more than a year ago and which Congress has been grappling with ever since.

The second is legislation to determine when and how St. Elizabeths Hospital will be transfered from the federal government to the city government.

In addition, Congress is expected to give final approval this week to the city's budget and federal appropriations for the fiscal year that already started this month.

A few smaller pieces involving the District appear to be headed toward enactment, as well:

*A measure to raise the limit on the jurisdiction of the D.C. small-claims court from $750 to $2,000 is expected to be given final approval by the House today. That bill also provides for a review of the qualifications of retired D.C. judges before they can take on new cases.

*The Senate last week passed and sent to the president a measure to enable the Jewish War Veterans national memorial to keep its property tax exemption even though the group's headquarters has moved.

Sen. Paula Hawkins (R-Fla.) said the memorial had made a "good faith effort" to resolve the issue at the local level but that the District's Department of Finance and Revenue had denied an application for continuation of the exemption. Hawkins said it was appropriate for Congress to step in because the memorial was chartered by Congress.

*The Senate also gave final approval to a resolution authorizing the Kahlil Gibran Centennial Foundation to establish a memorial on federal land in the District or its environs to commemorate the Lebanese-born poet who wrote "The Prophet."

The site is to be selected by the Interior Secretary, the National Capital Planning Commission and the Commission of Fine Arts. The foundation would pay the cost of building the memorial, a sculpture of some sort, and the Interior Department would be responsible for maintaining it.

The home rule measure would change the way Congress reviews and may disapprove D.C. laws under the decade-old act that gave the District self-government. Under the original act, it took only the vote of one house to veto criminal legislation and two houses to veto noncriminal legislation.

But this method was ruled invalid by the U.S. Supreme Court in June 1983, casting a shadow over the city's authority to govern itself and in the process preventing it from issuing bonds to finance operations.

The corrective legislation would require any disapproval to be accomplished by a majority vote of both houses and signature of the president.

That measure, which the White House has said the president will sign, has been tacked onto two pieces of legislation that are wending their way through Congress, the District's fiscal 1985 appropriations bill and the federal government's catch-all spending resolution for agencies whose regular appropriations bills have not been passed.

The St. Elizabeths legislation requires just one final vote from the House for it to be sent to the president for signing, and congressional aides said this probably would happen today.

The House approved the measure once last week, but the Senate added an amendment on how to deal with hospital property not used for mental health purposes. The House would have to pass on that change.

The legislation would turn over operation of the massive mental hospital in Southeast Washington to the District in October 1987 and would provide for $219 million in federal payments to the city over a six-year transition period ending in 1991.