Barring one long-shot bid for the crucial testimony of a former South Korean diplomat, the House's congressional bribery investigation is about to sputter to an inconclusive end.

With little of success, the State Department has agreed to try to set up a meeting of two House committee members with South Korean President Park Chung Hee in an effort to obtain the testimony of Park's onetime adviser, Kim Dong Jo, former ambassador here, according to sources.

Leon Jaworski, special counsel to the House Committee on Standards of Official Conduct, has said that his probe would be only half complete without Kim's cooperation.

With his testimony, investigators are known to feel that they may have cases against several more sitting members of congress for serious violations.

Businessman Tongsun Park has already testified that he made more than $750,000 in payments, mostly cash, to some members of Congress.

Kim's testimony was sought to show that members who have said they could'nt know Park was a Korean Central Intelligence Agency operative would have no such excuse about diplomat Kim, who is suspected of having made or directed payments to as many as 10 current House members.

The Korean goverment, citing diplomatic immunity has balked at making him available to testify, despite a House vote to cut out off economic aid to Seoul in retail item.

Investigators feel that without Kim's testimony there is nothing left to do. The 18-month probe would then be completed after producing four charges of ethics violation among sitting House members.

The committee voted on July 12 to bring disciplinary proceedings against Reps. John J. McFall, Edward Roybal and Charles H. Wilson, all California Democreats, and Edward J. Patten (D.N.J.).

Sources said the decision to try once again for Kim's testimony was made yesterday at a meeting including House Speaker Thomas (Tip) O'Neill (D-Mass.), Deputy Secretary of State Warren Christopher, Minority Leader John Rhodes (R-Ariz.) and Reps. Floyd Spence (R-S.C.) and Lee Hamilton (D-Ind.), Spence and Hamilton are to be the committee's representative to President Park, should a meeting be set up.

Kim Dong Jo quit as a foreign policy adviser to Park in June, citing the trouble his involvement in the case had caused the country.

Because he then became a private citizen, there was hope that Kim might be able to testify. Since then, however, there has been no sign of cooperation despite the pressure of the aid cutoff decision and a number of concessions made by Jaworski to get the testimony, including agreeing that it would not have to be sworn.