The Supreme Court yesterday agreed to review an Oregon ruling overturning the manslaughter conviction of James E. Bradshaw because he had been questioned improperly (Oregon vs. Bradshaw).

In other actions, the court:

* Agreed to consider a decision (INS vs. Phinpathya) that makes it easier for aliens to travel abroad and still remain eligible for a hardship exemption.

* Said it will decide whether states may tax bank shares based on the bank's total assets without excluding from that asset tally all federal securities owned by the bank (American Bank and Trust, Et Al vs. Dallas County, et al).

* Agreed to take up a case involving the rights of illegitimate children to receive Social Security benefits (Jones vs. Schweiker).

* Refused to rule in a case involving whether sex education in public schools violates religious freedoms (Smith vs. Ricci).

* Affirmed a lower court ruling upholding Alabama's plan to hold its legislative elections Tuesday using a controversial interim redistricting scheme (Burton vs. Hobbie).

* Said it would decide what, if any, power states have to regulate liquor sales on Indian reservations within their borders (Rice vs. Rehner).

* Refused to get involved in deciding whether a state may bar legal clinics unless each named partner in the firm is admitted to practice in the state.

* Refused to free the Chase Manhattan Bank from paying about $450,000 to Vietnamese who had deposited the money in the bank's Saigon branch.

* Declined to judge the constitutionality of a Louisiana law that triggered the release of accused killer Charles Walgamotte.

* Let stand a ruling that the Ohio Legislature, not the courts, has the ultimate power to decide whether water in the state should be flouridated.

* Declined to step into a water rights spat in the West over whether the first person to file an application for water use has a superior right to that water.

* Let stand a ruling upholding a Massachusetts' law requiring reports on the names, ages and addresses of children attending private schools.

* Declined to review a ruling that legal services lawyers may be paid when they bring civil rights suits against local and state officials.

* Left intact a court-ordered freeze on federal highway funds for Pennsylvania imposed as a penalty for its failure to set up a state auto emissions testing program.

* Asked the Department of Justice for its views on a court-ordered interm redistricting plan for Mississippi's five congressional seats.

* Left intact the conviction of John F. Gibson, a former secretary-treasurer of the Hotel and Restaurant Employes and Bartenders International Union.

* Rejected appeals from five death-row inmates in Georgia and Florida, including one who contested his sentence because he was shackled in leg irons while the jury considered his punishment.