The Supreme Court yesterday turned down former representative George V. Hansen's appeal of his 1984 felony conviction for filing false financial disclosure statements, clearing the way for the seven-term Idaho Republican to begin serving his 5- to 15-month prison sentence.

The court also declined to hear an appeal by television anchorwoman Christine Craft, who sued her former television station for demoting her after allegedly telling her she was "too old, unattractive and not deferential enough to men." Two jury verdicts for up to $500,000 against the station were overturned on appeal.

Craft, now 41 and an anchorwoman at a television station in Sacramento, Calif., sued Kansas City television station KMBC-TV in 1983 for sex discrimination and fraud. A jury awarded her $500,000 in damages against Metromedia, Inc., but that award was thrown out by the trial judge.

A second federal jury awarded Craft $325,000 in damages for fraud, but that award was overturned last June by the 8th U.S. Circuit Court of Appeals, which said she had not sufficiently proven her fraud allegations.

Craft said yesterday she was disappointed but that she felt her legal battle had "done a lot" for women reporters, "even if only news directors and editors are more cautious in their wording."

Justice Sandra Day O'Connor alone voted to hear Craft's appeal, but four of the nine justices must vote to hear a case.

Hansen, 54, who faces a $40,000 fine in addition to the jail sentence, told reporters yesterday he still had the option of seeking a new trial or a reduced sentence, but knowledgeable observers said yesterday such requests are rarely granted.

A federal jury here convicted Hansen in April 1984 of failing to record $334,000 in profits and loans -- including transactions involving Texas financier Nelson Bunker Hunt -- on financial reports to the House of Representatives as required under the 1978 Ethics in Government Act. Hansen is the only public official to have been prosecuted for such false statements.

The justices, without comment, declined to review his arguments that Congress never intended criminal penalties for violating the ethics law, which requires high government officials to list their incomes, assets and liabilities.

Hansen lost a reelection bid to Democrat Richard Stallings by 170 votes. Hansen's wife, Connie, is now running for the seat.

Sen. Orrin G. Hatch (R-Utah), with 123 other lawmakers, supported Hansen's arguments.

The court also agreed yesterday to hear four cases next term, including a 1984 appeals court ruling that President Reagan illegally used a "pocket veto" in 1983 to kill a bill linking military aid in El Salvador to human rights progress there.

The challenge, led by Rep. Michael D. Barnes (D-Md.), puts the court once more in the position of refereeing a political struggle between the legislative and executive branches.

The framers of the Constitution allowed the president 10 working days to act on legislation. It automatically becomes law if he fails to act while Congress is in session.

However, in a reversal of normal procedure, bills passed fewer than 10 days before Congress adjourns are "pocket vetoed" if the president fails to act.

There have been growing complaints over the years that pocket vetoes are unconstitutional during short adjournments, such as between sessions of the same Congress.

Opponents argue that the framers allowed the pocket veto because they saw Congress transacting its business and adjourning for relatively long periods of several months before the next session.

The pocket veto, according to those arguments, was intended only to avoid long periods of uncertainty about legislation that fell between two Congresses or two sessions of the same Congress.

The Supreme Court in 1929 upheld President Calvin Coolidge's use of a pocket veto, but opponents argue that in recent years both houses of Congress have appointed representatives to accept messages from the president during adjournments of the same Congress and the president can no longer contend he is unable to return a bill when Congress is not in session.

The case, Burke v. Barnes, will be argued next fall.

The justices also agreed to resolve questions left in the court's 1983 rulng, INS v. Chadha, striking down as unconstitutional the "one-house" or legislative veto.

Hundreds of federal laws contained such provisions, which enabled either the House or the Senate to decide unilaterally whether any of a wide range of governmental regulatory actions would take effect.

The question in Alaska Airlines, Inc. v. Brock is: Under what conditions the legislative veto provisions of a bill can be severed, leaving the remainder of the bill intact? The case, to be argued next fall, involves a secion of the Airline Deregulation Act of 1978, which established reemployment protection for some airline employes.

In other action, the court rejected an appeal by Alvin C. Copeland, owner of Popeye's Famous Fried Chicken, who said a Louisiana Supreme Court order that he scale down a Christmas display at his home would violate his rights to free speech and freedom of religion.