¹"our former alienated condition": literally "when we were in the flesh." Paul's perspective, of course, is from the now obtaining redeemed state of his and his listeners' existence.
²Literally: "The passions of sins through the Law were active in our members (body)." I take this to mean that something beyond our control was taking place within us and that somehow the Law was one factor in that process.
³Literally: "to the end of bearing fruit for death." I take this to mean that the behavior thus described is ultimately self-destructive and/or destructive of others, at the very least futile.
⁴Literally: "having died in that where we were coerced." In other passages Paul speaks of sinners dying with Christ and rising to new life in a new existence that is free from sin.
⁵Literally: "we serve in newness of spirit and not in oldness of letter." I take this to mean that in the New Covenant existence one no longer obeys God by observing precepts of the written law but through direct discernment of and obedience to God's will as mediated by the Holy Spirit.
⁶I am translating Paul's noun ἁμαρτία, a feminine singular abstract, as "sinfulness" rather than as "Sin." Clearly he is not referring to an individual sinful act but to a state or behavioral tendency in the psyche. I am not going to comment on what Paul says about the role of the Law and the commandment in bringing sinfulness into action because it is not directly relevant to the parallelism with Mark that is my chief concern here. But I will note that I have chosen to translate the Greek form of the tenth commandment, οὐκ ἐπιθυμήσεις, as "You must not lust," although it is usually conveyed by "Thou shalt not covet," or perhaps more properly, "You must not desire what belongs to another or others." Although I realize that I may be rendering an expansive term much too specifically, I have chosen to convey the verb ἐπιθυμεῖν here as "lust" because it seems to me more meaningful in the context to understand the demonic character of this desire and how it could trigger temptation to sin.
⁷Being alive" and "dying" or "death" here are, of course, not literal in any sense of physical life and death; they are clearly spiritual experiences or experiences of psychic processes and states. I understand "being alive" here to refer to integrated and efficacious selfhood wherein the judgment and will are effectual and result in action according with one's intentions, while "dying" is the process of losing control over one's actions even as one may still discern and intend what is right and good, and "death" is the condition of impotence to effect what one discerns as right and good and intends to do.
⁸Literally: "but I am fleshly, having been sold into subjection to Sin." At play here is the conventional language of enslavement, slave-marketing and (ultimately) "redemption" or "buying back" of the slave to be a free person again. Here then "a slave sold into the power of Sinfulness" means that the speaker is no longer free to act according to his own intentions but is at the beck and call of a slave-master, Sinfulness, that compels him to perform actions that are self-destructive and destructive of others.
⁹This description goes the the heart of the experience of alienation as I am using the term: the judging and willing aspect of the psyche is split apart from the acting aspect, so that the actions performed are not recognizable as one's own deeds but as another's. Someone else seems to be in control of one's body and using it quite otherwise than as one intends.
¹⁰Here my translation is very close to being literal. Paul uses the Greek word οἰκεῖ, which I have translated "has (no) dwelling" in verse 18 and "is housed" in verse 20. This language seems very close to the image used by Jesus in Mark 3:27 of the house of the strong man who is first bound so that his house can be plundered. It is language consistent with the notion of possession, where an alien force or person seizes control of a body, as Apollo is said to seize control of the body of his prophetess, the Sibyl, at Delphi or elsewhere.
¹¹In the last five verses of the chapter the Greek noun νόμος is used in several different ways: (1) the Law (laid down by Moses) of God; (2) "governing principle" or "controlling factor" (a sort of automatic coercive force clicking into operation whenever one exerts one's will; (3) "ruling power"; this is the same as νόμος  in sense (2) but now it is represented as a personalized force exerting a will counter to one's own will; this appears to be the same as the next νόμος, "the ruling power of sinfulness present within me"-in verse 23 this is the general of an army laying siege to one's selfhood and then taking it captive in order to make it a slave to the general's superior, a ruler to whom one's selfhood is now subject. Finally in verse 25 νόμος is at first "God's (Mosaic) Law, but then must be conveyed in English by "rule" where it is both that automatic coercive force controlling one's behavior and at the same time a personified master whom one is obliged to serve.
¹²Literally: "the body of this death." I take this to mean "this self/body in which the real me is trapped and powerless to act according to my own intentions. The sense is much as that indicated earlier in verses 9-10, "Time was when for me there was no Law and I was alive, but when the commandment confronted me, sinfulness sprang into life, 10 and I died, realizing, to my chagrin, that the commandment intended to bring life actually brought about death." The body in which one resides is not a corpse that is can or should be buried, but it is "meat" (perhaps the real sense of Greek σάρξ, usually translated "flesh") to be manipulated by another or others rather than controlled by any power resident within it; in another sense the body or selfhood is a "corpse" because there is no real "life"-no growth or nourishment, no capacity to relate to other creatures, no hope whatsoever for any meaningful existence in the future.
¹³In this summation Paul gives perhaps the clearest expression in the entire passage to the nature of alienation: the psyche is riven into two parts, one an inner core that consents to God's will and that intends to perform it, the other a body or acting self that carries out acts that are evil, devastating to one's self and to others.