Immortality of soul after the Day of Judgment
The certain hope that God has given to all Christians who truly believe in Jesus is that we will have a glorious body (and the accompanying soul) that Jesus the man had after resurrection, since as his adopted brothers & sisters we have also died and risen with him in baptism.
Whatever St. Paul previously believed as a Pharisee, the above hope was what Paul must have believed as well, as a Christian. Paul was very clear in 1 Cor 15 (esp. vv. 54-55) that our glorified body is immortal. The early church believed this as well, as this is the final line of The Apostle's Creed:
I believe in ...
and the life everlasting. Amen.
As for the rest of the 2000 year history, I am not aware of any mainstream Christian denominations that don't believe in life everlasting for believers. Life everlasting for believers is quite a solid consensus. What's still debatable (since there is not enough Biblical data) is the fate of the souls of the damned: annihilation, temporary suffering in hell, everlasting suffering in hell in body+soul, everlasting suffering in hell in soul only, etc.
Whether one is a Christian mortalist or not, the result is the same: life everlasting. Thus for Christian mortalists one theory is that God would need to create an eternal soul from scratch while preserving some features of our earthly lives (taken from God's memory) to make our glorious bodies. For the non Christian mortalists, God would simply let the immortal soul to be hypostasized with the glorious body, thus enabling the soul to experience a new, glorious and eternal existence.
Status of the soul prior to the Day of Judgment
Many recent evangelicals believe in the conscious existence of the soul prior to the day of judgment, as my other answer made clear based on careful exegesis of the whole of the New Testament by Michael Bird using Biblical theology approach and using the latest research of Second Temple Judaism. He said that Paul wasn't as clear about the intermediate state as the final state, but he said we can make a good case that Paul believed in conscious existence in the intermediate state.
Catholic position is similar, but the believers's blessed presence in heaven with Christ during the intermediate state can be preceded by Purgatory.
In my opinion, it's the result that matters. In his letters Paul indicated the result, not the precise mechanism or precise ontology of body and soul. Depending on what the soul without the body is capable off (we only have theories) God may either let the soul to continue into the intermediate state without change, or God would need to fit that soul with a temporary partial something to experience Christ's presence and/or purgatory.
Christian mortalists who interpret Paul and the Biblical data differently will say that upon death, the soul is either unconscious or perishes along with the body.