Did the Jews kill Jesus ,or did the Romans pay the High Priest to have Jesus killed, like my Pastor says?
During the time of the Roman occupation, the Jewish people did not have the right to execute anyone. Jesus was executed for violating Roman law (claiming to be a king). He was executed by Roman soldiers, by order of the Roman Procurator, Pontius Pilate, using the Roman means of execution, crucifixion. The Jewish method of execution was stoning.
All these facts are easily verifiable in both Biblical and historical accounts.
In fairness, Pilate tried repeatedly to get Jesus freed, but the Jewish people who were present demanded that he apply the law. He finally surrendered to their wishes and had Jesus executed.