Which one you need will depend on the context.

“Atonement” refers to the repair of a relationship (“reconciliation” is often a very good substitute), by dealing with –esp. paying for or making up for SIN (offense) against another, esp. God. The English word “at-one-ment” was coined to underline the idea of reconciling, uniting parties at odds with each other. The Hebrew word it translated (KOFER) may originally have had to do with “covering” something (the offense) so that it is no longer seen and held against the offender.

“Redemption” refers to reclaiming or “buying” someone, particularly by paying a very high price OR performing a difficult work. (“Ransom” may also be used for this.) For example, Israel was “redeemed” out of Egypt, rescued/reclaimed from Pharaoh’s power, by the MIGHTY acts of God. It CAN and often DOES refer to rescuing someone from sin or its punishment, and so to atonement, though not always.

“Salvation” is the most general of all these terms, referring to rescue from a negative situation, of whatever sort. It MAY be used for “salvation from sins”, that is rescue from sin, esp. from its consequences, and so . Notice the similarity to “redemption”.

“Expiation” refers to the paying to make up from something, as of a price or debt incurred.

“Propitiation” (which you did not include) is the making of a payment to satisfy the ANGER of the one who was offended, and so to the making of PEACE between the parties.

These two terms are used to speak of different aspects of “atoning sacrifice”. Sometimes “atonement” refers to one or the other of these, sometimes to BOTH. Given your choices, “expiation” may be the best option in the list (though again, the full idea should include both).

“Repentance” is a bit different from all the others — the sorrowful turning AWAY from the sin, acknowledging the wrong and turning to the right thing (which may include actions to repair the damage done – restitution or expiation). It is a necessary and important and part of HOW one benefits from atonement, receives salvation etc., though it is not the atonement itself. Rabbinic Judaism makes much of this, and so it is possible that some Jewish materials may loosely present “repentance” and “atonement” as synonyms.

So, again, if we’re using the terms in the BROADEST sense, “redemption” would likely work best. If the focus is on the specific thing done to deal with the sin “expiation” is the best option in your list.

“Repentance” means “remorse or contrition for past conduct or sin.”