Several conservative Republican senators agreed yesterday to support a judicial candidate whose nomination they had delayed with a detailed questionnaire seeking his views on such issues as abortion, school prayer and the Equal Rights Amendment.

The senators expressed support for Joseph H. Rodriguez, President Reagan's nominee for a federal judgeship in New Jersey, during a Senate Judiciary Committee hearing that featured sharp partisan exchanges about the propriety of the questionnaire.

Sen. Orrin G. Hatch (R-Utah), one of three conservatives who signed the eight-page document, said he is satisfied with Rodriguez's answers and intends to support him.

Sen. Jeremiah Denton (R-Ala.) said in a letter that he plans to vote for Rodriguez, and the third signatory, Sen. John P. East (R-N.C.), did not attend the hearing.

Chairman Strom Thurmond (R-S.C.) also said he would vote for Rodriguez and predicted that the committee will confirm him next Thursday.

But the growing support for Rodriguez, one of 114 federal judges whom Reagan will appoint this year, did not quell the charges that some conservatives were trying to impose a political litmus test on judicial nominees.

Hatch defended the questionnaire, which asked, among other things, whether Rodriguez believes "that a 'viable' fetus is a human being" and sought a list of his political contributions for the last 10 years.

Hatch said some of the queries "may seem ideological."

But, he said, "Every one of those questions was legitimate . . . . I have never used a single litmus test or a single case . . . to disqualify any nominee to the federal bench."

Sen. Howard M. Metzenbaum (D-Ohio), calling the questionnaire "very offensive," said it went "far beyond the bounds of propriety."

"What is supposed to be the right answer about abortion, school prayer and gun control?" he asked. "My answer, your answer or someone else's answer? What is the right wing of this country demanding from our judicial nominees?"

Sen. Paul Simon (D-Ill.) told Rodriguez that the nominee "ba- sically ducked the questions and, in my opinion, you did the right thing."

Hatch and Thurmond questioned Rodriguez about issues raised in the questionnaire, including gun control, judicial activism and the death penalty.

Thurmond asked about a case in which the New Jersey public advocate's office, which Rodriguez heads, had argued that "the death penalty is a meaningless gesture of pure revenge."

Rodriguez responded cautiously, as he did in the questionnaire, in some instances saying only that he would follow the Constitution or that he could not comment on pending cases.

Rodriguez assured Hatch that he would impose the death penalty in cases where it was le- gally warranted, saying he always "supported the law, whether people have liked it or disliked it."

Thurmond said that the panel's Democrats and Republicans should agree on a standard questionnaire for judicial nominees and that individual senators should not send out their own questions after a nominee has testified before the committee.