This may be related to another question about the parable that is the context for this question on Matthew 18:34 in particular.
OP: What is the original word used in our oldest manuscripts and how has that word been traditionally used?
The word used here for "torturers" is τοῖς βασανισταῖς or, in its lexical form, βασανιστής (basanistēs). There are no textual variants in the manuscript tradition affecting this word/reading (if that is what lies behind the question about "oldest manuscripts").
As you will see from the Liddell-Scott-Jones lexion entry linked, it has a reasonably wide range meaning, from one who "examines by close questioning" (so, "interrogator", I suppose) through to outright "torturer".
This is the only occurrence of this noun in the Greek Bible (Septuagint [LXX], or NT); the related verb form is used about 41 times in the LXX and NT.1 In LXX 1 Sam 5:3 (= "1 Kingdoms") it appears in an interesting "plus", in which God torments the Philistines who have taken away the Ark of the Covenant. (The rest of the LXX occurrences are in 2 Maccabees (4x), and 4 Maccabees (19x!).) In the NT, it is also used, for example, of various torments in the book of Revelation (9:5; 11:10; 12:2; 14:10; 20:10).
The word has a history, of course.2 It was used of inspection of coins, and this meaning co-existed alongside being "tormented" by disease, through to the more harrowing kind of testing that involves the rack, and so on.
OP: What exactly is meant by this word "torture" in this specific passage?
It looks like it means what it says: the unmerciful servant is being "tormented" as a result of his lack of forgiving-ness. Schneider (see note 2, p. 563) simply states that it means "tormenter" rather than "tester" without further discussion - presumably because that more benign meaning would make no sense in the context of the parable.
Donald Hagner has some useful comment on this verse:3
Torturers, though disallowed by Jews, were common in Roman prisons; in the case of unpaid debt, friends and relations would have accordingly been more urgent in raising money. Given the enormity of the debt, the imprisonment would have been permanent.This together with the reference to the torturers may hint (cf. v 35) at eschatological punishment.
And, of course, it needs to be remembered that Jesus is drawing this word-picture in a parable.
OP: I find this disturbing, as these are Christ's own words.
Jesus is recorded in the gospels as saying many disturbing things, and it seems especially so in some of Luke's parables. Compare this to, e.g. Luke 12:47 on hearing and not doing, or Luke 19:27 when the king slaughters those who rejected him, or Luke 20:16 on the tenants in the vineyard. Jesus not so gentle, meek, and mild.
- The related verb form is βασανίζω (basanizō).
- Here I'm drawing on the useful article by Johannes Schneider, "βάσανος, etc.", in Theological Dictionary of the New Testament, ed. by G. Kittel & G. Friedrich (Eerdmans, 1964), vol. 1, pp. 561-563.
- D. A. Hagner, Matthew 14-28 (Word Biblical Commentary, 33B; Dallas: Word, 1995), p. 540.